Scenario

Based on 2022 Singapore HDB resale price (real-life) data sets, your team is supposed to construct a multiple regression model (for one particular district) to explain the HDB resale price (ResalePrice) in dollars with the given independent variables.

Marking Criteria

Documentation and Presentation: 10 marks

Methodology: 10 marks

R-codes, computer outputs interpretation and graphical explanations: 15 marks

Recommendations and conclusions: 15 marks

Format:

Written Report: PDF Format: Within 10pages excluding the cover page and Appendix

Appendix: codes with computer outputs

You are required to provide the detailed documentation of how you search your recommended model for inference purpose and justify each step in your data analysis. You are also expected to provide model assumption justification and hypothesis testing evidences (R-codes and computer outputs) with clear explanations that your recommended model is the best model among all the models considered according to BIC criterion. Based on your final recommended model, state clearly your recommendations and conclusions.

Part 1 of Project

Load Data In

Sengkang1 <- read.csv("data/Sengkang2023P.csv", stringsAsFactors = TRUE)

head(Sengkang1, 5)
##      Date   Type Block           Street    Story Area   Model LeaseBegin        LeaseRemain
## 1 2022-01 3 ROOM  331C    ANCHORVALE ST 10 TO 12   67 Model A       2015 92 years 09 months
## 2 2022-01 3 ROOM  209C COMPASSVALE LANE 16 TO 18   67 Model A       2011 88 years 11 months
## 3 2022-01 3 ROOM  211C COMPASSVALE LANE 10 TO 12   68 Model A       2013 90 years 02 months
## 4 2022-01 3 ROOM  467B    FERNVALE LINK 04 TO 06   68 Model A       2016 93 years 08 months
## 5 2022-01 3 ROOM  414B    FERNVALE LINK 07 TO 09   68 Model A       2016  93 years 01 month
##   ResalePrice
## 1      420000
## 2      418000
## 3      410000
## 4      382000
## 5      410000

For visualisation purposes and model creation ideas

library(httr)
geocode <- function(block, streetname) {
  base_url <- "https://developers.onemap.sg/commonapi/search"
  address <- paste(block, streetname, sep = " ")
  query <- list("searchVal" = address, 
                "returnGeom" = "Y",
                "getAddrDetails" = "N",
                "pageNum" = "1")
  
  res <- GET(base_url, query = query)
  restext<-content(res, as="text")
  
  output <- jsonlite::fromJSON(restext)  %>% 
    as.data.frame() %>%
    dplyr::select("results.LATITUDE", "results.LONGITUDE")
  return(output)
}
Sengkang$LATITUDE <- 0
Sengkang$LONGITUDE <- 0

for (i in 1:nrow(Sengkang)){
  temp_output <- geocode(Sengkang[i, 3], Sengkang[i, 4])
  
  Sengkang$LATITUDE[i] <- temp_output$results.LATITUDE
  Sengkang$LONGITUDE[i] <- temp_output$results.LONGITUDE
}
write_rds(Sengkang, file ="Sengkang_coords")
Sengkang <- read_rds("Sengkang_coords")
Sengkang_sf <- st_as_sf(Sengkang, coords = c("LONGITUDE", "LATITUDE"), crs = 4326) |>
    st_transform(crs = 3414)

glimpse(Sengkang_sf)
## Rows: 2,116
## Columns: 11
## $ Date        <chr> "2022-01", "2022-01", "2022-01", "2022-01", "2022-01", "2022-01", "2022-01", "…
## $ Type        <chr> "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM", "3 ROOM"…
## $ Block       <chr> "331C", "209C", "211C", "467B", "414B", "467A", "414B", "414B", "453A", "472B"…
## $ Street      <chr> "ANCHORVALE ST", "COMPASSVALE LANE", "COMPASSVALE LANE", "FERNVALE LINK", "FER…
## $ Story       <chr> "10 TO 12", "16 TO 18", "10 TO 12", "04 TO 06", "07 TO 09", "19 TO 21", "16 TO…
## $ Area        <int> 67, 67, 68, 68, 68, 68, 68, 68, 67, 68, 67, 67, 68, 67, 67, 68, 68, 68, 67, 68…
## $ Model       <chr> "Model A", "Model A", "Model A", "Model A", "Model A", "Model A", "Model A", "…
## $ LeaseBegin  <int> 2015, 2011, 2013, 2016, 2016, 2016, 2016, 2016, 2015, 2016, 2015, 2015, 2017, …
## $ LeaseRemain <chr> "92 years 09 months", "88 years 11 months", "90 years 02 months", "93 years 08…
## $ ResalePrice <int> 420000, 418000, 410000, 382000, 410000, 408000, 412000, 400000, 405000, 350000…
## $ geometry    <POINT [m]> POINT (34282.7 41941.51), POINT (35328.82 40660.61), POINT (35341.91 407…
library(tmap)
sengkang_sp <- Sengkang_sf %>%
  mutate(subzone = as.factor(ifelse(grepl("^1", Block), "Rivervale",
                          ifelse(grepl("^2", Block), "Compassvale",
                                 ifelse(grepl("^3", Block), "Anchorvale",
                                        ifelse(grepl("4", Block), "Fernvale", "others"))))),
         Date = lubridate::ym(Date),
         LeaseBegin = lubridate::ym( paste0(LeaseBegin,"-01")),
         years_used = as.numeric((Date - LeaseBegin)/365)) %>%
    as_Spatial()
  
tmap_mode("view")
## tmap mode set to interactive viewing
tm_shape(sengkang_sp) +
  tm_dots(col = "subzone")

Initial regression with original dataset

L0 <- lm(ResalePrice ~., 
         data = Sengkang1)
summary(L0)
## 
## Call:
## lm(formula = ResalePrice ~ ., data = Sengkang1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -104398  -10412       0   10782   74298 
## 
## Coefficients: (38 not defined because of singularities)
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    135214.5    71692.3   1.886 0.059503 .  
## Date2022-02                      -471.3     3390.7  -0.139 0.889468    
## Date2022-03                     -2206.6     4379.5  -0.504 0.614449    
## Date2022-04                      2319.3     5457.1   0.425 0.670892    
## Date2022-05                      -604.7     6502.8  -0.093 0.925921    
## Date2022-06                      1159.1     7731.2   0.150 0.880843    
## Date2022-07                      1113.0     8904.3   0.125 0.900542    
## Date2022-08                       852.0    10162.7   0.084 0.933198    
## Date2022-09                      6211.8    11555.1   0.538 0.590958    
## Date2022-10                      3538.0    12893.7   0.274 0.783819    
## Date2022-11                      7377.6    14140.1   0.522 0.601931    
## Date2022-12                      6234.2    15435.3   0.404 0.686355    
## Type4 ROOM                      52840.0    19613.6   2.694 0.007146 ** 
## Type5 ROOM                     127382.5    34636.9   3.678 0.000245 ***
## Block104                         2235.5    33937.7   0.066 0.947490    
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## Block265B                       93788.2    50217.5   1.868 0.062028 .  
## Block265C                       77434.5    46071.5   1.681 0.093043 .  
## Block265D                       47327.5    64624.4   0.732 0.464083    
## Block266A                       71926.2    61725.4   1.165 0.244118    
## Block266B                       61930.6    70179.1   0.882 0.377682    
## Block267A                      510351.0   127685.7   3.997 6.76e-05 ***
## Block267B                      509148.6   127287.6   4.000 6.68e-05 ***
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## Block268B                      567912.2   129558.2   4.383 1.26e-05 ***
## Block268C                      486194.4   126206.2   3.852 0.000122 ***
## Block268D                      525691.3   129550.4   4.058 5.24e-05 ***
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## Block269B                      533178.8   128564.0   4.147 3.58e-05 ***
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## Block269D                      506139.5   129340.8   3.913 9.56e-05 ***
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## Block273D                       59348.8    66556.4   0.892 0.372708    
## Block274A                      101192.5    55103.6   1.836 0.066517 .  
## Block274B                      115757.8    55906.9   2.071 0.038590 *  
## Block274C                      132564.6    56027.5   2.366 0.018119 *  
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## Block275B                       37454.0    69973.2   0.535 0.592557    
## Block275C                       33622.0    70160.6   0.479 0.631863    
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## Block277D                       46010.7    68861.4   0.668 0.504143    
## Block278A                      114401.5    55511.1   2.061 0.039505 *  
## Block278B                      111284.3    55286.4   2.013 0.044326 *  
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## Block279A                      -73411.8    85434.6  -0.859 0.390341    
## Block279B                       29621.2    82142.6   0.361 0.718449    
## Block279C                      -94197.6    83357.6  -1.130 0.258659    
## Block280A                      -31008.7    82215.8  -0.377 0.706112    
## Block280B                      -29603.2    82172.7  -0.360 0.718712    
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## Block281B                      -21099.9    81953.2  -0.257 0.796861    
## Block282B                       12475.2    81757.8   0.153 0.878747    
## Block282C                       28462.2    81519.1   0.349 0.727033    
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## Block286C                       46589.3    54965.8   0.848 0.396808    
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## Block287B                       50152.6    55308.4   0.907 0.364684    
## Block287C                       42511.4    54699.2   0.777 0.437185    
## Block288A                       50147.8    54824.3   0.915 0.360512    
## Block288B                       57471.7    54853.4   1.048 0.294948    
## Block288C                       39284.2    54722.6   0.718 0.472956    
## Block289A                       60903.2    54627.4   1.115 0.265098    
## Block289B                       44909.6    54660.1   0.822 0.411440    
## Block290A                      182216.4    60190.4   3.027 0.002514 ** 
## Block290B                      135279.5    56179.1   2.408 0.016173 *  
## Block290C                      130569.5    58653.4   2.226 0.026170 *  
## Block291A                      116299.1    52379.0   2.220 0.026561 *  
## Block291B                      154322.3    59631.5   2.588 0.009759 ** 
## Block291D                      134417.3    52731.1   2.549 0.010909 *  
## Block292A                      154538.4    58347.7   2.649 0.008177 ** 
## Block292B                      141892.6    56640.1   2.505 0.012356 *  
## Block293A                      -30497.9    65603.7  -0.465 0.642092    
## Block293B                      -28998.1    65599.7  -0.442 0.658526    
## Block293C                      -38577.6    65344.1  -0.590 0.555037    
## Block293D                      -26117.7    65556.8  -0.398 0.690400    
## Block294A                      -34868.7    65599.9  -0.532 0.595135    
## Block295A                      133266.2    58268.6   2.287 0.022344 *  
## Block295B                      117018.1    58284.7   2.008 0.044874 *  
## Block295C                      180922.7    59841.3   3.023 0.002547 ** 
## Block296A                      139016.8    57775.1   2.406 0.016254 *  
## Block296B                      152182.1    58092.9   2.620 0.008901 ** 
## Block296C                      132402.5    60150.4   2.201 0.027891 *  
## Block297A                      128010.1    55458.3   2.308 0.021137 *  
## Block297B                      140106.6    51663.9   2.712 0.006775 ** 
## Block298A                      130182.1    50390.2   2.583 0.009885 ** 
## Block298B                      167939.8    51445.2   3.264 0.001124 ** 
## Block298C                      130580.8    51670.3   2.527 0.011611 *  
## Block298D                      118636.4    50250.6   2.361 0.018372 *  
## Block299A                      112659.1    50141.8   2.247 0.024813 *  
## Block299B                      127234.5    52521.0   2.423 0.015543 *  
## Block299C                      134625.2    52442.9   2.567 0.010363 *  
## Block301A                      152834.3    55773.3   2.740 0.006219 ** 
## Block301B                      143977.6    51820.2   2.778 0.005538 ** 
## Block301C                      119387.5    53488.5   2.232 0.025777 *  
## Block301D                      123019.0    53061.7   2.318 0.020575 *  
## Block302A                       98479.4    54920.9   1.793 0.073178 .  
## Block302B                      -38427.9    65637.9  -0.585 0.558341    
## Block303A                      129723.5    52906.0   2.452 0.014334 *  
## Block303B                      172254.8    52040.5   3.310 0.000957 ***
## Block303C                      175958.0    53669.9   3.279 0.001070 ** 
## Block304A                      163353.6    58203.0   2.807 0.005078 ** 
## Block304B                      139632.8    56277.6   2.481 0.013217 *  
## Block305A                      152374.5    59063.2   2.580 0.009989 ** 
## Block305B                      120341.4    56708.1   2.122 0.034009 *  
## Block305C                      121200.1    55571.1   2.181 0.029356 *  
## Block306A                      164419.5    61576.8   2.670 0.007672 ** 
## Block306C                      147568.9    56906.2   2.593 0.009611 ** 
## Block307A                      106507.5    54260.9   1.963 0.049865 *  
## Block307C                      141626.8    56289.9   2.516 0.011984 *  
## Block308A                      130297.3    63147.0   2.063 0.039265 *  
## Block308B                      124348.3    55519.2   2.240 0.025270 *  
## Block308C                      135931.4    58035.4   2.342 0.019314 *  
## Block309A                      241142.1    71101.0   3.392 0.000715 ***
## Block309B                      191733.0    67725.6   2.831 0.004708 ** 
## Block309C                      224911.6    72831.4   3.088 0.002055 ** 
## Block309D                      220511.9    70366.7   3.134 0.001763 ** 
## Block310B                      188489.9    74029.1   2.546 0.011002 *  
## Block311A                      183205.1    67716.0   2.705 0.006906 ** 
## Block311B                      166496.8    69343.3   2.401 0.016482 *  
## Block311C                      183977.5    71092.8   2.588 0.009761 ** 
## Block311D                      223567.9    70749.8   3.160 0.001613 ** 
## Block312A                      136378.2    73265.9   1.861 0.062902 .  
## Block312B                      160431.9    73080.1   2.195 0.028312 *  
## Block313A                      212070.3    85705.0   2.474 0.013467 *  
## Block313B                      184885.9    83915.3   2.203 0.027745 *  
## Block313C                      233527.5    79046.3   2.954 0.003188 ** 
## Block314A                      228385.0    79418.2   2.876 0.004094 ** 
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## Block314C                      225963.3    81594.4   2.769 0.005694 ** 
## Block314D                      273508.6    81743.4   3.346 0.000843 ***
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## Block315B                      229097.9    81141.1   2.823 0.004821 ** 
## Block315C                      238822.0    80250.2   2.976 0.002972 ** 
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## Block316B                      247531.8    79148.2   3.127 0.001801 ** 
## Block317A                      215161.5    80352.7   2.678 0.007502 ** 
## Block317B                      206884.6    81526.8   2.538 0.011272 *  
## Block317C                      215750.9    79114.9   2.727 0.006473 ** 
## Block317D                      269046.5    78293.8   3.436 0.000607 ***
## Block318A                      290510.0    80708.3   3.600 0.000330 ***
## Block318B                      202497.4    80830.1   2.505 0.012354 *  
## Block318C                      215339.6    80347.0   2.680 0.007449 ** 
## Block319A                      201783.6    71275.1   2.831 0.004708 ** 
## Block319B                      174295.1    67245.8   2.592 0.009647 ** 
## Block319C                      201827.1    67998.9   2.968 0.003049 ** 
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## Block320D                      230121.8    72084.2   3.192 0.001443 ** 
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## Block322A                      213756.3    65188.0   3.279 0.001068 ** 
## Block322B                      203114.6    61509.0   3.302 0.000984 ***
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## Block324B                      265722.8    79043.7   3.362 0.000796 ***
## Block324D                      275180.1    77961.4   3.530 0.000430 ***
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## Block325B                      248624.4    77410.3   3.212 0.001350 ** 
## Block325C                      230038.2    76109.7   3.022 0.002554 ** 
## Block326A                     -117520.4    86725.7  -1.355 0.175618    
## Block326B                     -135994.0    86670.8  -1.569 0.116861    
## Block326C                     -131980.8    86119.2  -1.533 0.125623    
## Block326D                     -123319.5    87103.9  -1.416 0.157071    
## Block327A                     -157352.0    89090.1  -1.766 0.077586 .  
## Block327C                     -144632.7    86669.7  -1.669 0.095392 .  
## Block329A                     -144415.7    82331.7  -1.754 0.079644 .  
## Block329B                     -134843.8    83195.0  -1.621 0.105290    
## Block330A                     -133885.5    81422.8  -1.644 0.100341    
## Block330B                     -124449.5    81917.2  -1.519 0.128943    
## Block331A                     -133729.6    81374.2  -1.643 0.100534    
## Block331B                      -88922.6    83771.4  -1.061 0.288656    
## Block331C                     -131103.5    81606.9  -1.607 0.108392    
## Block332A                     -131722.9    84206.0  -1.564 0.117982    
## Block332B                     -131937.7    83696.6  -1.576 0.115172    
## Block332C                     -126902.8    84621.3  -1.500 0.133937    
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## Block333B                     -129896.4    85151.7  -1.525 0.127375    
## Block333C                     -128307.7    83897.7  -1.529 0.126415    
## Block333D                     -132554.0    84141.2  -1.575 0.115403    
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## Block334B                      -87989.5    77042.5  -1.142 0.253619    
## Block334C                      -92721.8    78382.5  -1.183 0.237041    
## Block335A                      -82482.3    77095.3  -1.070 0.284867    
## Block335B                      -75825.8    78435.6  -0.967 0.333853    
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## Block336B                      -87719.3    78186.3  -1.122 0.262093    
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## Block336D                      -76121.9    78243.8  -0.973 0.330786    
## Block338A                       67143.5    51272.4   1.310 0.190572    
## Block338B                       55109.6    51055.9   1.079 0.280603    
## Block338C                       28951.3    50974.6   0.568 0.570159    
## Block338D                       82018.9    51264.1   1.600 0.109848    
## Block403A                      288015.0    94928.4   3.034 0.002459 ** 
## Block403B                      290421.1    91711.2   3.167 0.001576 ** 
## Block403C                      285920.6    97023.9   2.947 0.003265 ** 
## Block403D                      229397.3    99913.0   2.296 0.021830 *  
## Block404A                      295186.3    94456.9   3.125 0.001815 ** 
## Block404B                      212662.8    95561.9   2.225 0.026219 *  
## Block405B                      260176.5    92323.5   2.818 0.004901 ** 
## Block405C                      302899.0    91782.4   3.300 0.000991 ***
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## Block406B                      309647.4   106336.0   2.912 0.003650 ** 
## Block406C                      298777.1   106293.2   2.811 0.005012 ** 
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## Block408A                      316174.2   105175.7   3.006 0.002694 ** 
## Block408B                      330023.7   100222.2   3.293 0.001017 ** 
## Block408C                      358390.6   107889.1   3.322 0.000918 ***
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## Block411B                      -13341.7    55092.9  -0.242 0.808687    
## Block412A                      307047.3    93243.2   3.293 0.001017 ** 
## Block412B                      282464.9    96553.1   2.925 0.003497 ** 
## Block413A                      256315.8    94471.9   2.713 0.006749 ** 
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## Block415A                      -74643.7    76286.3  -0.978 0.328017    
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## Block418C                       58789.9    50466.1   1.165 0.244249    
## Block430A                     -201192.4    85160.7  -2.363 0.018293 *  
## Block430B                     -171204.2    85143.1  -2.011 0.044546 *  
## Block430C                     -185537.0    85287.7  -2.175 0.029771 *  
## Block430D                     -177451.6    84932.0  -2.089 0.036864 *  
## Block432A                     -208120.1    93732.9  -2.220 0.026560 *  
## Block432B                     -205044.9    93803.4  -2.186 0.028994 *  
## Block433A                     -189040.8    96682.8  -1.955 0.050757 .  
## Block433B                     -195675.5    93743.6  -2.087 0.037043 *  
## Block434A                       28830.2    50518.9   0.571 0.568311    
## Block434B                       26866.6    49001.5   0.548 0.583589    
## Block435A                       26387.7    49261.6   0.536 0.592279    
## Block435B                       35971.9    50096.7   0.718 0.472851    
## Block435C                       31060.0    51937.8   0.598 0.549925    
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## Block436B                      -59042.9    60025.4  -0.984 0.325472    
## Block436C                      -36466.7    59095.6  -0.617 0.537285    
## Block438A                       19483.1    48927.0   0.398 0.690540    
## Block438B                     -164207.1    86384.5  -1.901 0.057529 .  
## Block439A                       37278.9    48692.4   0.766 0.444047    
## Block439B                     -147191.9    92319.4  -1.594 0.111085    
## Block439C                     -116765.4    97938.3  -1.192 0.233378    
## Block440A                     -157140.5    83463.5  -1.883 0.059949 .  
## Block440B                     -147530.8    82884.0  -1.780 0.075306 .  
## Block440C                     -164930.9    83780.0  -1.969 0.049201 *  
## Block441A                      -56372.7    69864.7  -0.807 0.419875    
## Block441B                      -91791.3    69471.6  -1.321 0.186632    
## Block441C                      -53320.5    65284.6  -0.817 0.414221    
## Block441D                      -54166.9    74909.0  -0.723 0.469742    
## Block443A                      -21984.3    55041.5  -0.399 0.689652    
## Block443B                      -13959.7    54898.1  -0.254 0.799315    
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## Block445A                       -3541.4    55897.7  -0.063 0.949493    
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## Block446B                       26245.4    45138.1   0.581 0.561035    
## Block446C                      -15519.0    55045.6  -0.282 0.778041    
## Block447A                       39090.1    45038.5   0.868 0.385588    
## Block448A                     -210721.1    97479.3  -2.162 0.030816 *  
## Block448B                     -194547.0    98623.6  -1.973 0.048742 *  
## Block450A                     -215661.3    98006.5  -2.200 0.027941 *  
## Block450B                     -185376.5    98631.9  -1.879 0.060394 .  
## Block451A                     -189371.4    85762.9  -2.208 0.027406 *  
## Block451B                     -180589.5    85535.7  -2.111 0.034931 *  
## Block452A                     -172119.2    85237.7  -2.019 0.043654 *  
## Block452B                     -172938.6    86288.9  -2.004 0.045249 *  
## Block453A                     -157816.2    83035.5  -1.901 0.057568 .  
## Block453B                     -161054.0    83053.1  -1.939 0.052688 .  
## Block453C                     -160248.0    83133.5  -1.928 0.054114 .  
## Block453D                     -147216.3    83466.2  -1.764 0.077994 .  
## Block467A                      -93066.2    68787.7  -1.353 0.176298    
## Block467B                      -95807.5    68295.0  -1.403 0.160892    
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## Block468B                      -87453.7    69673.2  -1.255 0.209623    
## Block468C                      -91150.3    68555.5  -1.330 0.183879    
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## Block469B                      -86697.7    68836.6  -1.259 0.208078    
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## Block470A                      -96446.5    67221.4  -1.435 0.151586    
## Block470B                      -94988.5    67901.6  -1.399 0.162068    
## Block470C                      -98872.6    67494.3  -1.465 0.143179    
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## Block471B                      -83718.8    68518.8  -1.222 0.221982    
## Block471C                      -79906.8    68283.0  -1.170 0.242114    
## Block472A                      -60768.3    67856.5  -0.896 0.370657    
## Block472B                      -76466.2    67740.8  -1.129 0.259180    
## Block472C                      -72875.6    67770.4  -1.075 0.282418    
## Block473A                      -78514.5    71475.7  -1.098 0.272191    
## StreetANCHORVALE DR                  NA         NA      NA       NA    
## StreetANCHORVALE LANE                NA         NA      NA       NA    
## StreetANCHORVALE LINK                NA         NA      NA       NA    
## StreetANCHORVALE RD                  NA         NA      NA       NA    
## StreetANCHORVALE ST                  NA         NA      NA       NA    
## StreetCOMPASSVALE BOW                NA         NA      NA       NA    
## StreetCOMPASSVALE CRES               NA         NA      NA       NA    
## StreetCOMPASSVALE DR                 NA         NA      NA       NA    
## StreetCOMPASSVALE LANE               NA         NA      NA       NA    
## StreetCOMPASSVALE LINK               NA         NA      NA       NA    
## StreetCOMPASSVALE RD                 NA         NA      NA       NA    
## StreetCOMPASSVALE ST                 NA         NA      NA       NA    
## StreetCOMPASSVALE WALK               NA         NA      NA       NA    
## StreetFERNVALE LANE                  NA         NA      NA       NA    
## StreetFERNVALE LINK                  NA         NA      NA       NA    
## StreetFERNVALE RD                    NA         NA      NA       NA    
## StreetFERNVALE ST                    NA         NA      NA       NA    
## StreetJLN KAYU                       NA         NA      NA       NA    
## StreetRIVERVALE CRES                 NA         NA      NA       NA    
## StreetRIVERVALE DR                   NA         NA      NA       NA    
## StreetRIVERVALE ST                   NA         NA      NA       NA    
## StreetRIVERVALE WALK                 NA         NA      NA       NA    
## StreetSENGKANG CTRL                  NA         NA      NA       NA    
## StreetSENGKANG EAST AVE              NA         NA      NA       NA    
## StreetSENGKANG EAST RD               NA         NA      NA       NA    
## StreetSENGKANG EAST WAY              NA         NA      NA       NA    
## StreetSENGKANG WEST AVE              NA         NA      NA       NA    
## StreetSENGKANG WEST WAY              NA         NA      NA       NA    
## Story04 TO 06                   25826.9     2241.4  11.522  < 2e-16 ***
## Story07 TO 09                   47402.4     2235.5  21.205  < 2e-16 ***
## Story10 TO 12                   50795.2     2290.4  22.178  < 2e-16 ***
## Story13 TO 15                   58879.1     2212.6  26.610  < 2e-16 ***
## Story16 TO 18                   72417.6     2813.3  25.742  < 2e-16 ***
## Story19 TO 21                   67083.9     4054.2  16.547  < 2e-16 ***
## Story22 TO 24                   76787.4     4611.7  16.651  < 2e-16 ***
## Story25 TO 27                   73484.8     6188.6  11.874  < 2e-16 ***
## Area                             2383.5      764.7   3.117 0.001867 ** 
## ModelModel A                    14764.4     3244.0   4.551 5.81e-06 ***
## ModelModel A2                        NA         NA      NA       NA    
## ModelPremium Apartment               NA         NA      NA       NA    
## LeaseBegin                           NA         NA      NA       NA    
## LeaseRemain75 years 03 months   13185.3    32710.8   0.403 0.686948    
## LeaseRemain75 years 04 months  -25239.7    40074.0  -0.630 0.528913    
## LeaseRemain75 years 05 months   35728.2    37333.5   0.957 0.338737    
## LeaseRemain75 years 06 months    8163.5    39280.8   0.208 0.835398    
## LeaseRemain75 years 07 months    4803.0    38561.0   0.125 0.900893    
## LeaseRemain75 years 08 months     554.5    37786.9   0.015 0.988295    
## LeaseRemain75 years 09 months   -8471.4    38833.7  -0.218 0.827349    
## LeaseRemain75 years 10 months  -13030.3    38303.4  -0.340 0.733769    
## LeaseRemain75 years 11 months  -41236.9    38680.5  -1.066 0.286573    
## LeaseRemain76 years             -1313.4    40936.1  -0.032 0.974409    
## LeaseRemain76 years 01 month    -7069.7    40325.3  -0.175 0.860856    
## LeaseRemain76 years 02 months   -5701.6    41595.3  -0.137 0.890994    
## LeaseRemain76 years 03 months  -32214.5    42057.5  -0.766 0.443831    
## LeaseRemain76 years 04 months  -46821.6    43524.0  -1.076 0.282224    
## LeaseRemain76 years 05 months  -53271.9    43687.1  -1.219 0.222906    
## LeaseRemain76 years 06 months  -55370.2    44176.0  -1.253 0.210277    
## LeaseRemain76 years 07 months  -55774.5    45750.8  -1.219 0.223022    
## LeaseRemain76 years 08 months  -70629.9    46236.6  -1.528 0.126851    
## LeaseRemain76 years 09 months  -80201.3    47090.5  -1.703 0.088773 .  
## LeaseRemain76 years 10 months  -82596.6    48578.9  -1.700 0.089312 .  
## LeaseRemain76 years 11 months  -83540.1    49530.0  -1.687 0.091900 .  
## LeaseRemain77 years            -76948.6    51146.8  -1.504 0.132694    
## LeaseRemain77 years 01 month   -80159.5    51520.4  -1.556 0.119971    
## LeaseRemain77 years 02 months  -99233.6    52575.0  -1.887 0.059311 .  
## LeaseRemain77 years 03 months  -88741.5    53288.6  -1.665 0.096085 .  
## LeaseRemain77 years 04 months  -90678.2    54037.4  -1.678 0.093565 .  
## LeaseRemain77 years 05 months -108147.0    55527.6  -1.948 0.051666 .  
## LeaseRemain77 years 06 months -120952.2    56272.7  -2.149 0.031780 *  
## LeaseRemain77 years 07 months -114989.4    57187.2  -2.011 0.044549 *  
## LeaseRemain77 years 08 months -113515.0    58501.2  -1.940 0.052540 .  
## LeaseRemain77 years 09 months -134690.7    59837.5  -2.251 0.024549 *  
## LeaseRemain77 years 10 months -137906.4    60881.9  -2.265 0.023661 *  
## LeaseRemain77 years 11 months -148388.5    62010.8  -2.393 0.016849 *  
## LeaseRemain78 years           -132337.9    63276.0  -2.091 0.036675 *  
## LeaseRemain78 years 01 month  -139203.8    64098.0  -2.172 0.030049 *  
## LeaseRemain78 years 02 months -145582.0    65163.1  -2.234 0.025638 *  
## LeaseRemain78 years 03 months -154977.0    66297.5  -2.338 0.019553 *  
## LeaseRemain78 years 04 months -159300.1    67525.9  -2.359 0.018461 *  
## LeaseRemain78 years 05 months -172362.4    68814.1  -2.505 0.012370 *  
## LeaseRemain78 years 06 months -172829.7    71031.9  -2.433 0.015098 *  
## LeaseRemain78 years 07 months -157083.7    71250.4  -2.205 0.027645 *  
## LeaseRemain78 years 08 months -171340.4    72262.5  -2.371 0.017875 *  
## LeaseRemain78 years 09 months -179444.1    74024.9  -2.424 0.015476 *  
## LeaseRemain78 years 10 months -188942.2    75376.6  -2.507 0.012305 *  
## LeaseRemain78 years 11 months -171133.5    76427.8  -2.239 0.025308 *  
## LeaseRemain79 years           -191657.9    77618.1  -2.469 0.013663 *  
## LeaseRemain79 years 01 month  -183450.8    79581.0  -2.305 0.021305 *  
## LeaseRemain79 years 02 months -209419.8    80178.3  -2.612 0.009103 ** 
## LeaseRemain79 years 03 months -188180.0    82655.3  -2.277 0.022961 *  
## LeaseRemain79 years 04 months -176720.3    83551.2  -2.115 0.034603 *  
## LeaseRemain79 years 05 months -216351.3    84472.6  -2.561 0.010539 *  
## LeaseRemain79 years 06 months -223733.3    85586.7  -2.614 0.009045 ** 
## LeaseRemain79 years 07 months -236027.8    87027.6  -2.712 0.006770 ** 
## LeaseRemain79 years 08 months -228235.0    87620.0  -2.605 0.009293 ** 
## LeaseRemain79 years 09 months -235583.6    89625.0  -2.629 0.008672 ** 
## LeaseRemain79 years 10 months -237592.8    90591.8  -2.623 0.008822 ** 
## LeaseRemain79 years 11 months -227788.2    92153.1  -2.472 0.013564 *  
## LeaseRemain80 years           -222994.3    93143.3  -2.394 0.016797 *  
## LeaseRemain80 years 01 month  -246676.5    94422.0  -2.612 0.009088 ** 
## LeaseRemain80 years 02 months -240987.5    95430.7  -2.525 0.011675 *  
## LeaseRemain80 years 03 months -272119.3    97303.8  -2.797 0.005237 ** 
## LeaseRemain80 years 04 months -269702.3    98621.6  -2.735 0.006325 ** 
## LeaseRemain80 years 05 months -268617.6    99667.5  -2.695 0.007123 ** 
## LeaseRemain80 years 06 months -248951.0   101720.2  -2.447 0.014515 *  
## LeaseRemain80 years 07 months -300030.1   103616.8  -2.896 0.003845 ** 
## LeaseRemain80 years 08 months -276533.5   103628.8  -2.669 0.007710 ** 
## LeaseRemain80 years 09 months -202986.7   110084.2  -1.844 0.065413 .  
## LeaseRemain80 years 10 months -293615.6   106083.4  -2.768 0.005721 ** 
## LeaseRemain80 years 11 months -279974.6   108360.4  -2.584 0.009878 ** 
## LeaseRemain81 years           -264229.4   110387.0  -2.394 0.016816 *  
## LeaseRemain81 years 01 month  -284504.8   111323.2  -2.556 0.010707 *  
## LeaseRemain81 years 02 months -288020.2   113818.1  -2.531 0.011502 *  
## LeaseRemain81 years 03 months -294508.1   114351.5  -2.575 0.010116 *  
## LeaseRemain81 years 04 months -298456.9   114926.7  -2.597 0.009508 ** 
## LeaseRemain81 years 05 months -279721.5   117288.6  -2.385 0.017221 *  
## LeaseRemain81 years 06 months -332002.0   118577.4  -2.800 0.005185 ** 
## LeaseRemain81 years 07 months -334194.0   120502.9  -2.773 0.005625 ** 
## LeaseRemain81 years 08 months -307547.4   121188.1  -2.538 0.011267 *  
## LeaseRemain81 years 09 months -353040.0   123357.3  -2.862 0.004275 ** 
## LeaseRemain81 years 10 months -359052.4   123940.3  -2.897 0.003828 ** 
## LeaseRemain81 years 11 months -324702.8   125523.8  -2.587 0.009791 ** 
## LeaseRemain82 years           -355135.3   127080.3  -2.795 0.005270 ** 
## LeaseRemain82 years 01 month  -345273.5   128163.6  -2.694 0.007147 ** 
## LeaseRemain82 years 02 months -345291.3   130372.3  -2.649 0.008179 ** 
## LeaseRemain82 years 03 months -383366.0   131891.5  -2.907 0.003712 ** 
## LeaseRemain82 years 04 months -425762.8   134359.0  -3.169 0.001565 ** 
## LeaseRemain82 years 05 months -409517.6   134869.7  -3.036 0.002440 ** 
## LeaseRemain82 years 06 months -404799.4   137287.9  -2.949 0.003247 ** 
## LeaseRemain82 years 07 months -394375.3   137253.3  -2.873 0.004125 ** 
## LeaseRemain82 years 08 months -399714.4   138230.4  -2.892 0.003893 ** 
## LeaseRemain82 years 09 months -419698.9   139508.4  -3.008 0.002675 ** 
## LeaseRemain82 years 10 months -417229.7   140788.8  -2.964 0.003095 ** 
## LeaseRemain82 years 11 months -449938.9   142191.5  -3.164 0.001589 ** 
## LeaseRemain83 years           -451998.9   143709.4  -3.145 0.001696 ** 
## LeaseRemain83 years 01 month  -451163.6   147677.2  -3.055 0.002294 ** 
## LeaseRemain83 years 02 months -427662.3   146771.7  -2.914 0.003629 ** 
## LeaseRemain83 years 10 months  105956.7    49973.4   2.120 0.034166 *  
## LeaseRemain83 years 11 months  141006.6    52923.1   2.664 0.007805 ** 
## LeaseRemain84 years             53570.9    45539.9   1.176 0.239661    
## LeaseRemain84 years 01 month    99297.1    48745.8   2.037 0.041840 *  
## LeaseRemain84 years 03 months  155746.9    60436.6   2.577 0.010070 *  
## LeaseRemain84 years 04 months   47732.2    49065.2   0.973 0.330810    
## LeaseRemain84 years 06 months   32120.8    33562.6   0.957 0.338718    
## LeaseRemain84 years 08 months   54899.7    44396.3   1.237 0.216457    
## LeaseRemain84 years 09 months   49618.6    29022.3   1.710 0.087556 .  
## LeaseRemain84 years 10 months        NA         NA      NA       NA    
## LeaseRemain84 years 11 months        NA         NA      NA       NA    
## LeaseRemain85 years 01 month    -8162.5    28211.2  -0.289 0.772369    
## LeaseRemain85 years 02 months        NA         NA      NA       NA    
## LeaseRemain85 years 05 months        NA         NA      NA       NA    
## LeaseRemain85 years 07 months  175028.1    54965.9   3.184 0.001484 ** 
## LeaseRemain85 years 08 months  207208.6    54527.9   3.800 0.000151 ***
## LeaseRemain85 years 09 months  142422.0    54187.9   2.628 0.008678 ** 
## LeaseRemain85 years 10 months  190543.8    61812.0   3.083 0.002093 ** 
## LeaseRemain85 years 11 months  133320.7    49105.9   2.715 0.006713 ** 
## LeaseRemain86 years            147296.5    50102.3   2.940 0.003339 ** 
## LeaseRemain86 years 01 month   198774.0    53959.3   3.684 0.000239 ***
## LeaseRemain86 years 02 months  142779.0    45826.3   3.116 0.001874 ** 
## LeaseRemain86 years 03 months  108422.1    45766.2   2.369 0.017974 *  
## LeaseRemain86 years 04 months  119009.5    41579.5   2.862 0.004272 ** 
## LeaseRemain86 years 05 months  124598.6    42972.5   2.899 0.003798 ** 
## LeaseRemain86 years 06 months  126001.9    39823.6   3.164 0.001591 ** 
## LeaseRemain86 years 07 months  114688.4    39298.9   2.918 0.003577 ** 
## LeaseRemain86 years 08 months  190010.4    45494.8   4.177 3.15e-05 ***
## LeaseRemain86 years 09 months   91368.6    37094.3   2.463 0.013896 *  
## LeaseRemain86 years 10 months  127326.4    40185.8   3.168 0.001567 ** 
## LeaseRemain86 years 11 months   88350.6    35490.6   2.489 0.012915 *  
## LeaseRemain87 years             93112.6    34535.2   2.696 0.007101 ** 
## LeaseRemain87 years 01 month    82571.7    36938.0   2.235 0.025553 *  
## LeaseRemain87 years 02 months   46760.1    35215.0   1.328 0.184452    
## LeaseRemain87 years 03 months   59483.0    30125.4   1.975 0.048526 *  
## LeaseRemain87 years 04 months   36327.9    35292.9   1.029 0.303511    
## LeaseRemain87 years 05 months   48434.6    28961.8   1.672 0.094684 .  
## LeaseRemain87 years 06 months  183237.0    81159.8   2.258 0.024121 *  
## LeaseRemain87 years 07 months   36974.0    32576.1   1.135 0.256575    
## LeaseRemain87 years 09 months  204192.8    71560.7   2.853 0.004391 ** 
## LeaseRemain87 years 11 months  172181.6    77082.7   2.234 0.025664 *  
## LeaseRemain88 years                  NA         NA      NA       NA    
## LeaseRemain88 years 01 month   151078.5    57245.8   2.639 0.008408 ** 
## LeaseRemain88 years 02 months  178220.8    60873.5   2.928 0.003472 ** 
## LeaseRemain88 years 03 months  146997.1    51321.8   2.864 0.004245 ** 
## LeaseRemain88 years 04 months  147888.1    53208.4   2.779 0.005521 ** 
## LeaseRemain88 years 05 months  167269.3    54874.6   3.048 0.002347 ** 
## LeaseRemain88 years 06 months  159328.5    51097.4   3.118 0.001858 ** 
## LeaseRemain88 years 07 months  132630.5    50290.8   2.637 0.008453 ** 
## LeaseRemain88 years 08 months  136409.4    51341.7   2.657 0.007979 ** 
## LeaseRemain88 years 09 months  115687.3    44113.6   2.622 0.008827 ** 
## LeaseRemain88 years 10 months  107649.4    48359.6   2.226 0.026177 *  
## LeaseRemain88 years 11 months  115373.8    41357.7   2.790 0.005350 ** 
## LeaseRemain89 years             95658.2    34347.7   2.785 0.005427 ** 
## LeaseRemain89 years 01 month    95425.6    36268.3   2.631 0.008607 ** 
## LeaseRemain89 years 02 months   50054.7    38065.6   1.315 0.188746    
## LeaseRemain89 years 03 months   68606.5    30061.9   2.282 0.022633 *  
## LeaseRemain89 years 04 months   71711.6    29487.4   2.432 0.015147 *  
## LeaseRemain89 years 05 months   75159.2    28397.8   2.647 0.008223 ** 
## LeaseRemain89 years 06 months   68703.5    28508.7   2.410 0.016089 *  
## LeaseRemain89 years 07 months   68950.3    25946.2   2.657 0.007966 ** 
## LeaseRemain89 years 08 months   54615.2    24953.5   2.189 0.028790 *  
## LeaseRemain89 years 09 months   49968.4    24587.3   2.032 0.042319 *  
## LeaseRemain89 years 10 months   48599.8    24327.6   1.998 0.045947 *  
## LeaseRemain89 years 11 months   47443.3    21851.7   2.171 0.030093 *  
## LeaseRemain90 years             39302.2    21689.9   1.812 0.070207 .  
## LeaseRemain90 years 01 month    38486.8    21829.2   1.763 0.078112 .  
## LeaseRemain90 years 02 months   32978.2    19591.0   1.683 0.092540 .  
## LeaseRemain90 years 04 months   23697.5    19374.3   1.223 0.221489    
## LeaseRemain90 years 05 months   16318.5    22521.5   0.725 0.468838    
## LeaseRemain90 years 06 months   29084.1    26127.8   1.113 0.265842    
## LeaseRemain90 years 07 months        NA         NA      NA       NA    
## LeaseRemain90 years 08 months  260349.5    87180.9   2.986 0.002874 ** 
## LeaseRemain90 years 09 months  260246.1    89200.9   2.918 0.003586 ** 
## LeaseRemain90 years 11 months  256348.6    88103.3   2.910 0.003678 ** 
## LeaseRemain91 years            249977.9    81941.6   3.051 0.002328 ** 
## LeaseRemain91 years 01 month   255037.0    79481.8   3.209 0.001364 ** 
## LeaseRemain91 years 02 months  255307.1    78056.0   3.271 0.001099 ** 
## LeaseRemain91 years 03 months  255401.8    80424.9   3.176 0.001529 ** 
## LeaseRemain91 years 04 months  250298.1    75169.3   3.330 0.000892 ***
## LeaseRemain91 years 05 months  253094.2    73871.0   3.426 0.000631 ***
## LeaseRemain91 years 06 months  242598.0    72029.9   3.368 0.000778 ***
## LeaseRemain91 years 07 months  235473.6    70678.7   3.332 0.000887 ***
## LeaseRemain91 years 08 months  241540.8    69757.5   3.463 0.000552 ***
## LeaseRemain91 years 09 months  221764.8    68013.3   3.261 0.001139 ** 
## LeaseRemain91 years 10 months  236604.6    67005.0   3.531 0.000428 ***
## LeaseRemain91 years 11 months  229205.5    65707.3   3.488 0.000502 ***
## LeaseRemain92 years            230143.1    63926.9   3.600 0.000330 ***
## LeaseRemain92 years 01 month   212874.9    62969.9   3.381 0.000744 ***
## LeaseRemain92 years 02 months  210340.7    61497.1   3.420 0.000644 ***
## LeaseRemain92 years 03 months  209203.1    60228.8   3.473 0.000530 ***
## LeaseRemain92 years 04 months  193956.3    58945.7   3.290 0.001026 ** 
## LeaseRemain92 years 05 months  192731.9    57571.2   3.348 0.000837 ***
## LeaseRemain92 years 06 months  180248.8    56706.9   3.179 0.001513 ** 
## LeaseRemain92 years 07 months  179204.0    55083.3   3.253 0.001169 ** 
## LeaseRemain92 years 08 months  174156.5    53832.9   3.235 0.001245 ** 
## LeaseRemain92 years 09 months  169729.1    53301.2   3.184 0.001484 ** 
## LeaseRemain92 years 10 months  156142.6    51184.7   3.051 0.002328 ** 
## LeaseRemain92 years 11 months  154266.0    50210.9   3.072 0.002166 ** 
## LeaseRemain93 years            151152.2    48904.0   3.091 0.002037 ** 
## LeaseRemain93 years 01 month   154763.9    47725.1   3.243 0.001212 ** 
## LeaseRemain93 years 02 months  149786.7    46394.4   3.229 0.001274 ** 
## LeaseRemain93 years 03 months  144847.1    45546.0   3.180 0.001505 ** 
## LeaseRemain93 years 04 months  129777.3    44263.0   2.932 0.003425 ** 
## LeaseRemain93 years 05 months  135808.0    42840.3   3.170 0.001558 ** 
## LeaseRemain93 years 06 months  121350.7    41402.7   2.931 0.003436 ** 
## LeaseRemain93 years 07 months  113865.4    40450.7   2.815 0.004950 ** 
## LeaseRemain93 years 08 months  110442.0    39649.9   2.785 0.005420 ** 
## LeaseRemain93 years 09 months  103354.2    38699.1   2.671 0.007660 ** 
## LeaseRemain93 years 10 months  104672.5    37482.5   2.793 0.005303 ** 
## LeaseRemain93 years 11 months   99525.2    36567.7   2.722 0.006579 ** 
## LeaseRemain94 years             76572.4    34918.4   2.193 0.028485 *  
## LeaseRemain94 years 01 month    89373.6    33975.3   2.631 0.008621 ** 
## LeaseRemain94 years 02 months   71068.8    33435.5   2.126 0.033721 *  
## LeaseRemain94 years 03 months   73767.6    31899.9   2.312 0.020901 *  
## LeaseRemain94 years 04 months   68688.7    31042.1   2.213 0.027081 *  
## LeaseRemain94 years 05 months   66417.4    30599.9   2.171 0.030141 *  
## LeaseRemain94 years 06 months   60837.4    29391.3   2.070 0.038650 *  
## LeaseRemain94 years 07 months   57954.2    28779.4   2.014 0.044234 *  
## LeaseRemain94 years 08 months   56748.4    27882.9   2.035 0.042021 *  
## LeaseRemain94 years 09 months   51267.8    27189.3   1.886 0.059564 .  
## LeaseRemain94 years 10 months   52711.6    26684.4   1.975 0.048429 *  
## LeaseRemain94 years 11 months   38509.6    26235.1   1.468 0.142373    
## LeaseRemain95 years             30487.6    25856.9   1.179 0.238569    
## LeaseRemain95 years 01 month    30637.7    25605.2   1.197 0.231694    
## LeaseRemain95 years 02 months   60046.8    25337.9   2.370 0.017935 *  
## LeaseRemain95 years 03 months   40800.5    32685.0   1.248 0.212138    
## LeaseRemain95 years 04 months   31607.2    32402.8   0.975 0.329512    
## LeaseRemain95 years 05 months        NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22860 on 1354 degrees of freedom
## Multiple R-squared:  0.9549, Adjusted R-squared:  0.9296 
## F-statistic: 37.71 on 761 and 1354 DF,  p-value: < 2.2e-16

From the regression above, we know that there are too many categorical variables to consider. We have to condense them accordingly. Since we have visualised each block on the map and designate their respective subzone. We can categorise them in this manner as each neighborhood will have close proximity to their own respective facilities, such as schools, malls, childcare centre, etc. We can then see which subzones relative effects and it can show which subzone is more popular or less popular. In addition, it will help reduce the perfect collinearity issue that this current regression has.

length(unique(Sengkang$Block))
## [1] 521
length(unique(Sengkang$Street))
## [1] 29
length(unique(Sengkang$LeaseRemain))
## [1] 226

We can see from the code chunk above that block, street and LeaseRemain has 521, 29 and 226 categorical variables.

Data Wrangling

We will use the lubridate package to adjust the year and calculate lease years used as a numeric rather than a categorical variable. Since years_used and LeaseRemain are perfected correlated, we will drop LeaseRemaind from the dataframe.

site, the HDB blocks are numbered by 100+, 200+, 300+ and 400+ in Rivervale, Compassvale, Anchorvale and Fernvale respectively.

df <- Sengkang1 %>%
  mutate(Date = lubridate::ym(Date),
         LeaseBegin = lubridate::ym( paste0(LeaseBegin,"-01")),
         years_used = as.numeric((Date - LeaseBegin)/365),
         subzone = ifelse(grepl("^1", Block), "Rivervale",
                          ifelse(grepl("^2", Block), "Compassvale",
                                 ifelse(grepl("^3", Block), "Anchorvale",
                                        ifelse(grepl("4", Block), "Fernvale", "others")))),
         .before = Street) %>%
  mutate(subzone= as.factor(subzone),
         Date = as.factor(Date)) %>%
  select(-LeaseRemain, -LeaseBegin)

Using leaseremain as a factor will generate too many binary variables. Convert them into years_used would be easier. Date and LeaseBegin variables must be in date type before substracting between the two. The output would be in (drtn) days and thus we have to set it to numeric set to years.

Find the relationship between independent variables and Resale Price

plot(df$Date, df$ResalePrice)

plot(df$Type, df$ResalePrice)

plot(df$Block, df$ResalePrice)

plot(df$years_used, df$ResalePrice)

plot(df$subzone, df$ResalePrice)

plot(df$Street, df$ResalePrice)

plot(df$Story, df$ResalePrice)

plot(df$Area, log(df$ResalePrice))

plot(df$Model, df$ResalePrice)

Run Regression

All variables

We will first calculate the BIC of the regression of all variables.

reg_all <- lm(ResalePrice ~ ., data = df)
BIC(reg_all)
## [1] 52085.02

Residual check

r <- residuals(reg_all)
plot(df$Date, r,
     xlab = "Date", ylab = "Residuals")

plot(df$Type, r,
     xlab = "Type", ylab = "Residuals")

plot(df$Block, r,
     xlab = "Block", ylab = "Residuals")

plot(df$years_used, r,
     xlab = "years_used", ylab = "Residuals")

plot(df$subzone, r,
     xlab = "subzone", ylab = "Residuals")

plot(df$Street, r,
     xlab = "Street", ylab = "Residuals")

plot(df$Story, r,
     xlab = "Story", ylab = "Residuals")

plot(df$Area, r,
     xlab = "Area", ylab = "Residuals")

plot(df$Model, r,
     xlab = "Model", ylab = "Residuals")

From the residual plots above, we notice all plots points are scattered around the residual =0. This suggesrt that the model assumptions are not violated. We have three types of location columns now, Block, Street and subzone. There should be high correlation between the X variables for these 3 variables, we will test the BIC number by dropping each variable out and picking the model with the lowest BIC ## Removing Block

L1 <- lm(ResalePrice ~ .-Block, data = df)
summary(L1)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -125199  -18458    -391   16605  127493 
## 
## Coefficients: (1 not defined because of singularities)
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             210695.6    22823.2   9.232  < 2e-16 ***
## Date2022-02-01            3068.6     3127.6   0.981 0.326637    
## Date2022-03-01            9561.5     3012.4   3.174 0.001525 ** 
## Date2022-04-01           19707.9     2957.8   6.663 3.43e-11 ***
## Date2022-05-01           22649.6     3022.6   7.493 9.91e-14 ***
## Date2022-06-01           30197.7     3101.4   9.737  < 2e-16 ***
## Date2022-07-01           34030.9     2899.1  11.738  < 2e-16 ***
## Date2022-08-01           35921.4     2959.2  12.139  < 2e-16 ***
## Date2022-09-01           46776.8     2968.3  15.759  < 2e-16 ***
## Date2022-10-01           54208.3     3198.9  16.946  < 2e-16 ***
## Date2022-11-01           56573.0     3172.8  17.831  < 2e-16 ***
## Date2022-12-01           63968.7     3084.1  20.742  < 2e-16 ***
## Type4 ROOM               49589.9     8541.6   5.806 7.41e-09 ***
## Type5 ROOM              111718.7    14907.3   7.494 9.85e-14 ***
## years_used               -7932.9      170.6 -46.503  < 2e-16 ***
## subzoneCompassvale       41771.1     8999.2   4.642 3.67e-06 ***
## subzoneFernvale         -19184.9     4668.2  -4.110 4.12e-05 ***
## subzoneRivervale        -34282.0     8746.1  -3.920 9.16e-05 ***
## StreetANCHORVALE DR      31753.6     6185.3   5.134 3.11e-07 ***
## StreetANCHORVALE LANE   -12441.5     7709.0  -1.614 0.106706    
## StreetANCHORVALE LINK    12221.1     4386.9   2.786 0.005388 ** 
## StreetANCHORVALE RD       -361.1     4641.1  -0.078 0.937990    
## StreetANCHORVALE ST       4879.3     5521.0   0.884 0.376923    
## StreetCOMPASSVALE BOW    49697.4    10253.2   4.847 1.35e-06 ***
## StreetCOMPASSVALE CRES  -35722.9     9568.3  -3.733 0.000194 ***
## StreetCOMPASSVALE DR     31509.0     9913.0   3.179 0.001502 ** 
## StreetCOMPASSVALE LANE  -31117.6     9936.8  -3.132 0.001763 ** 
## StreetCOMPASSVALE LINK   65221.1    10239.0   6.370 2.33e-10 ***
## StreetCOMPASSVALE RD      5531.1    10588.8   0.522 0.601478    
## StreetCOMPASSVALE ST    -34202.2    10359.9  -3.301 0.000978 ***
## StreetCOMPASSVALE WALK    2385.9    10932.0   0.218 0.827260    
## StreetFERNVALE LANE      11616.4     7948.8   1.461 0.144058    
## StreetFERNVALE LINK       8008.5     4145.7   1.932 0.053525 .  
## StreetFERNVALE RD        19886.0     4575.1   4.347 1.45e-05 ***
## StreetFERNVALE ST         6151.8     6283.4   0.979 0.327671    
## StreetJLN KAYU            6159.1     9980.8   0.617 0.537240    
## StreetRIVERVALE CRES     10162.6     9429.7   1.078 0.281284    
## StreetRIVERVALE DR       46191.2     9828.5   4.700 2.78e-06 ***
## StreetRIVERVALE ST       48896.7    11317.6   4.320 1.63e-05 ***
## StreetRIVERVALE WALK     73305.2    11396.4   6.432 1.56e-10 ***
## StreetSENGKANG CTRL      70136.4    10972.0   6.392 2.02e-10 ***
## StreetSENGKANG EAST AVE  66487.3    10535.5   6.311 3.39e-10 ***
## StreetSENGKANG EAST RD    1205.1    13776.8   0.087 0.930305    
## StreetSENGKANG EAST WAY  46129.6     6596.5   6.993 3.62e-12 ***
## StreetSENGKANG WEST AVE  31509.1     9286.4   3.393 0.000704 ***
## StreetSENGKANG WEST WAY       NA         NA      NA       NA    
## Story04 TO 06            25592.7     2314.5  11.058  < 2e-16 ***
## Story07 TO 09            42931.7     2287.7  18.767  < 2e-16 ***
## Story10 TO 12            48919.7     2365.3  20.682  < 2e-16 ***
## Story13 TO 15            57804.1     2288.3  25.261  < 2e-16 ***
## Story16 TO 18            66014.4     2852.9  23.139  < 2e-16 ***
## Story19 TO 21            62481.2     4257.8  14.674  < 2e-16 ***
## Story22 TO 24            70526.8     4802.6  14.685  < 2e-16 ***
## Story25 TO 27            64799.3     6652.8   9.740  < 2e-16 ***
## Area                      2752.4      327.1   8.413  < 2e-16 ***
## ModelModel A             10424.3     2968.2   3.512 0.000454 ***
## ModelModel A2            52537.4     5374.8   9.775  < 2e-16 ***
## ModelPremium Apartment   20248.3     2601.4   7.784 1.11e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29140 on 2059 degrees of freedom
## Multiple R-squared:  0.8887, Adjusted R-squared:  0.8857 
## F-statistic: 293.6 on 56 and 2059 DF,  p-value: < 2.2e-16

Removing Street

L2 <- lm(ResalePrice ~ .-Street, 
         data = df)
summary(L2)
## 
## Call:
## lm(formula = ResalePrice ~ . - Street, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -108099  -10797       0   11327   83503 
## 
## Coefficients: (6 not defined because of singularities)
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             57717.8    56921.9   1.014 0.310747    
## Date2022-02-01           3205.0     2814.8   1.139 0.255040    
## Date2022-03-01           6466.2     2705.6   2.390 0.016970 *  
## Date2022-04-01          17158.8     2692.6   6.373 2.44e-10 ***
## Date2022-05-01          18814.9     2712.3   6.937 5.84e-12 ***
## Date2022-06-01          25490.1     2826.4   9.018  < 2e-16 ***
## Date2022-07-01          28758.1     2614.3  11.000  < 2e-16 ***
## Date2022-08-01          31702.8     2674.3  11.855  < 2e-16 ***
## Date2022-09-01          40950.6     2693.9  15.201  < 2e-16 ***
## Date2022-10-01          45604.4     2955.5  15.430  < 2e-16 ***
## Date2022-11-01          52303.1     2884.9  18.130  < 2e-16 ***
## Date2022-12-01          53873.6     2829.7  19.039  < 2e-16 ***
## Type4 ROOM              44773.9    18376.4   2.436 0.014941 *  
## Type5 ROOM             109528.5    32417.7   3.379 0.000746 ***
## Block104                38496.4    28571.1   1.347 0.178050    
## Block105                29117.8    20223.1   1.440 0.150115    
## Block106                12158.8    21354.2   0.569 0.569176    
## Block107                20476.7    19467.4   1.052 0.293034    
## Block108                22050.0    23269.1   0.948 0.343474    
## Block109                -5928.6    19034.0  -0.311 0.755482    
## Block112                36912.5    28595.6   1.291 0.196946    
## Block113                 9837.5    28592.5   0.344 0.730847    
## Block114                23623.2    23352.6   1.012 0.311891    
## Block115                -3738.4    21281.9  -0.176 0.860583    
## Block116A                7067.1    23750.3   0.298 0.766082    
## Block116B               15253.1    28877.6   0.528 0.597437    
## Block116C               19600.5    23678.2   0.828 0.407918    
## Block117A               30498.8    28900.2   1.055 0.291444    
## Block117B                6985.0    28797.4   0.243 0.808381    
## Block117C               -8221.0    21710.6  -0.379 0.704988    
## Block119A               76515.9    28645.3   2.671 0.007637 ** 
## Block119D               39860.5    28698.0   1.389 0.165040    
## Block120A               41046.0    28708.4   1.430 0.152986    
## Block120B               49664.9    28669.6   1.732 0.083413 .  
## Block121                -3589.3    20243.1  -0.177 0.859287    
## Block121A                2548.2    21621.5   0.118 0.906198    
## Block121C                 218.0    21571.1   0.010 0.991938    
## Block121D               -2607.4    21057.2  -0.124 0.901472    
## Block122               -17958.3    21572.7  -0.832 0.405280    
## Block122A               -5613.1    20845.0  -0.269 0.787750    
## Block122D               -8490.3    29604.6  -0.287 0.774312    
## Block122E              -18036.5    21132.1  -0.854 0.393506    
## Block123               -12474.1    19622.4  -0.636 0.525060    
## Block123A               23734.7    28569.0   0.831 0.406221    
## Block123B              -23287.1    20364.5  -1.144 0.252998    
## Block123C               -8667.4    28693.4  -0.302 0.762640    
## Block123D              -16957.1    23692.2  -0.716 0.474268    
## Block123E              -41107.1    28840.9  -1.425 0.154267    
## Block124                  806.2    23300.2   0.035 0.972401    
## Block124A                 175.7    19451.8   0.009 0.992794    
## Block124B               52519.1    22812.8   2.302 0.021455 *  
## Block124C               35324.0    22788.4   1.550 0.121323    
## Block125               -11127.2    20107.0  -0.553 0.580069    
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## Block153                41538.5    21584.6   1.924 0.054478 .  
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## Block162A               87940.9    19513.4   4.507 7.07e-06 ***
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## Block178A               56712.7    22036.5   2.574 0.010156 *  
## Block178B               35053.8    19306.2   1.816 0.069612 .  
## Block178C               59347.9    19574.9   3.032 0.002470 ** 
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## Block180A               75002.5    24250.5   3.093 0.002017 ** 
## Block180B               88954.2    20672.0   4.303 1.79e-05 ***
## Block180C               39599.1    19317.5   2.050 0.040540 *  
## Block180D               76942.2    20669.3   3.723 0.000204 ***
## Block183A              -24440.3    21031.2  -1.162 0.245372    
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## Block185B               24153.1    24335.8   0.992 0.321110    
## Block185C               39713.5    23522.7   1.688 0.091550 .  
## Block185D               40387.3    22196.8   1.820 0.069024 .  
## Block186A              -28361.0    24688.9  -1.149 0.250840    
## Block186B              -29657.2    21605.3  -1.373 0.170047    
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## Block188C              -47426.3    23695.6  -2.001 0.045512 *  
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## Block201C               41883.3    24581.8   1.704 0.088610 .  
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## Block202C               43756.9    22659.9   1.931 0.053659 .  
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## Block207D               47514.0    24939.3   1.905 0.056938 .  
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## Block224D               40313.0    21340.8   1.889 0.059074 .  
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## Block227A               50265.3    28584.6   1.758 0.078862 .  
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## Block228A              -18834.6    23720.6  -0.794 0.427303    
## Block228B               33269.3    19493.3   1.707 0.088075 .  
## Block228C               -9427.9    23725.2  -0.397 0.691142    
## Block229               -10554.5    21322.0  -0.495 0.620665    
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## Block246                55294.1    21610.0   2.559 0.010598 *  
## Block247                82054.6    25412.6   3.229 0.001268 ** 
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## Block253               -13889.5    28870.8  -0.481 0.630518    
## Block255               -16464.3    21562.8  -0.764 0.445248    
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## Block257B              126430.6    25415.1   4.975 7.25e-07 ***
## Block257C               58627.5    24542.1   2.389 0.017018 *  
## Block258A               67939.0    22658.4   2.998 0.002757 ** 
## Block258B               60081.1    22684.0   2.649 0.008163 ** 
## Block258C               41140.1    21630.0   1.902 0.057355 .  
## Block258D               50711.5    21017.0   2.413 0.015941 *  
## Block259A               40514.5    29613.5   1.368 0.171473    
## Block259B               71186.1    26150.2   2.722 0.006556 ** 
## Block259C               39999.0    29599.1   1.351 0.176774    
## Block260A              106882.8    22647.9   4.719 2.58e-06 ***
## Block260B              101399.7    29541.7   3.432 0.000614 ***
## Block260C               54778.8    21666.5   2.528 0.011560 *  
## Block260D              110941.5    24578.0   4.514 6.84e-06 ***
## Block261A               57022.0    21642.2   2.635 0.008502 ** 
## Block261B               63865.8    24553.9   2.601 0.009381 ** 
## Block261C              132499.4    29707.3   4.460 8.77e-06 ***
## Block262A               38339.6    20560.2   1.865 0.062403 .  
## Block262D               18712.2    24585.1   0.761 0.446699    
## Block264A              115974.3    24367.7   4.759 2.12e-06 ***
## Block264B              141542.2    24367.1   5.809 7.60e-09 ***
## Block264C              162392.9    29428.5   5.518 4.00e-08 ***
## Block264D              170407.9    29420.2   5.792 8.37e-09 ***
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## Block264F              176973.6    29322.9   6.035 1.97e-09 ***
## Block265A              200390.2    29428.8   6.809 1.39e-11 ***
## Block265B              147994.6    29409.7   5.032 5.41e-07 ***
## Block265C              121753.4    21397.3   5.690 1.51e-08 ***
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## Block268B              151842.4    29771.2   5.100 3.80e-07 ***
## Block268C              111732.5    21092.4   5.297 1.34e-07 ***
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## Block269B              143767.4    29797.7   4.825 1.54e-06 ***
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## Block271A              179836.6    20485.3   8.779  < 2e-16 ***
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## Block271C              190500.4    19722.4   9.659  < 2e-16 ***
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## Block272C              235304.2    22889.0  10.280  < 2e-16 ***
## Block272D              213010.4    22908.5   9.298  < 2e-16 ***
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## Block273D              224518.9    21214.4  10.583  < 2e-16 ***
## Block274A              203215.8    19654.0  10.340  < 2e-16 ***
## Block274B              210527.3    20957.6  10.045  < 2e-16 ***
## Block274C              228605.9    21225.8  10.770  < 2e-16 ***
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## Block275B              201715.7    22854.1   8.826  < 2e-16 ***
## Block275C              228017.4    21738.2  10.489  < 2e-16 ***
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## Block277C              235490.5    22721.7  10.364  < 2e-16 ***
## Block277D              217795.4    22869.5   9.523  < 2e-16 ***
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## Block278B              209188.8    19385.6  10.791  < 2e-16 ***
## Block278C              186153.0    21174.4   8.791  < 2e-16 ***
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## Block279B              265811.3    20562.4  12.927  < 2e-16 ***
## Block279C              147568.3    24474.7   6.029 2.05e-09 ***
## Block280A              218205.7    22192.9   9.832  < 2e-16 ***
## Block280B              205914.2    21375.3   9.633  < 2e-16 ***
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## Block281B              221507.1    20732.3  10.684  < 2e-16 ***
## Block282B              256403.9    20148.0  12.726  < 2e-16 ***
## Block282C              265148.3    19527.1  13.578  < 2e-16 ***
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## Block287C              140404.4    18399.9   7.631 4.02e-14 ***
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## Block288B              151291.2    18886.5   8.011 2.20e-15 ***
## Block288C              135862.4    18347.2   7.405 2.13e-13 ***
## Block289A              157307.3    18037.4   8.721  < 2e-16 ***
## Block289B              140295.3    18298.0   7.667 3.06e-14 ***
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## Block290B                2960.5    21606.2   0.137 0.891033    
## Block290C              -11680.4    24549.4  -0.476 0.634287    
## Block291A                6231.4    29564.0   0.211 0.833090    
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## Block291D               11047.5    21024.0   0.525 0.599329    
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## Block293A              127150.0    18907.7   6.725 2.45e-11 ***
## Block293B              131210.1    18936.9   6.929 6.17e-12 ***
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## Block293D              133481.4    19508.9   6.842 1.11e-11 ***
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## Block295B              -25933.5    21011.9  -1.234 0.217302    
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## Block298A                9256.4    19536.0   0.474 0.635699    
## Block298B               42330.9    22016.3   1.923 0.054697 .  
## Block298C               11613.6    21932.6   0.530 0.596524    
## Block298D                 466.0    19402.0   0.024 0.980842    
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## Block302B               57185.7    21322.2   2.682 0.007395 ** 
## Block303A                6393.3    24577.1   0.260 0.794796    
## Block303B               55995.8    22488.0   2.490 0.012876 *  
## Block303C               50962.8    23341.3   2.183 0.029156 *  
## Block304A               21252.5    22691.7   0.937 0.349121    
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## Block305B              -14107.3    22668.6  -0.622 0.533816    
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## Block307A              -20991.8    21653.3  -0.969 0.332469    
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## Block308A              -18656.1    29543.7  -0.631 0.527821    
## Block308B                 818.6    22675.7   0.036 0.971207    
## Block308C               -7924.9    20554.3  -0.386 0.699876    
## Block309A               60081.7    29694.0   2.023 0.043205 *  
## Block309B               23973.5    20581.1   1.165 0.244263    
## Block309C               49900.9    24203.6   2.062 0.039399 *  
## Block309D               39364.9    21099.3   1.866 0.062270 .  
## Block310B                6635.3    24387.9   0.272 0.785601    
## Block311A               10328.2    20000.7   0.516 0.605653    
## Block311B                8107.2    24446.4   0.332 0.740213    
## Block311C                 499.0    21298.1   0.023 0.981310    
## Block311D               31909.3    21356.2   1.494 0.135337    
## Block312A              -56128.6    29074.3  -1.931 0.053722 .  
## Block312B              -18861.7    29426.6  -0.641 0.521633    
## Block313A                1577.5    29587.7   0.053 0.957486    
## Block313B              -20841.5    24585.4  -0.848 0.396723    
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## Block314B               15830.8    22655.2   0.699 0.484798    
## Block314C               16152.7    29601.7   0.546 0.585371    
## Block314D               72049.0    29394.5   2.451 0.014350 *  
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## Block315B               17542.6    29604.6   0.593 0.553559    
## Block315C               28694.2    24581.4   1.167 0.243262    
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## Block316B               32641.1    24598.5   1.327 0.184715    
## Block317A                3925.4    22487.3   0.175 0.861446    
## Block317B               -1784.5    24430.4  -0.073 0.941779    
## Block317C               46973.6    29322.9   1.602 0.109369    
## Block317D               61131.2    24363.1   2.509 0.012201 *  
## Block318A               84576.4    29376.7   2.879 0.004043 ** 
## Block318B                7982.9    22646.6   0.352 0.724511    
## Block318C                9982.0    29530.1   0.338 0.735388    
## Block319A               35474.5    24688.6   1.437 0.150951    
## Block319B               14202.9    24488.9   0.580 0.562016    
## Block319C               28506.2    24613.5   1.158 0.246977    
## Block320A               79278.0    30912.1   2.565 0.010421 *  
## Block320B               20875.5    24572.2   0.850 0.395701    
## Block320D               69982.0    29530.1   2.370 0.017915 *  
## Block321A               38531.0    24570.4   1.568 0.117038    
## Block321B               42082.3    22678.2   1.856 0.063694 .  
## Block321C               35480.3    22648.5   1.567 0.117418    
## Block322A               62596.4    25824.5   2.424 0.015467 *  
## Block322B               47201.1    20944.0   2.254 0.024353 *  
## Block323B               56746.5    20251.7   2.802 0.005140 ** 
## Block323C               67112.5    24594.1   2.729 0.006427 ** 
## Block324A               86765.8    25423.3   3.413 0.000659 ***
## Block324B               81855.0    24632.8   3.323 0.000911 ***
## Block324D               79382.8    24593.9   3.228 0.001273 ** 
## Block325A               46143.8    21305.0   2.166 0.030471 *  
## Block325B               41046.7    20972.9   1.957 0.050509 .  
## Block325C               32346.6    21627.3   1.496 0.134949    
## Block326A              139137.4    21254.4   6.546 7.96e-11 ***
## Block326B              124744.9    20546.6   6.071 1.59e-09 ***
## Block326C              124992.3    19360.3   6.456 1.43e-10 ***
## Block326D              136322.6    21290.5   6.403 2.01e-10 ***
## Block327A               89144.4    29396.6   3.032 0.002465 ** 
## Block327C              108826.6    22445.0   4.849 1.37e-06 ***
## Block329A               96103.2    20469.0   4.695 2.90e-06 ***
## Block329B              106132.6    22055.0   4.812 1.64e-06 ***
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## Block330B              118340.8    20396.1   5.802 7.90e-09 ***
## Block331A              101937.0    18659.7   5.463 5.44e-08 ***
## Block331B              152420.2    29262.2   5.209 2.15e-07 ***
## Block331C              100060.5    21202.6   4.719 2.58e-06 ***
## Block332A              115476.7    21171.6   5.454 5.70e-08 ***
## Block332B              118638.4    19487.8   6.088 1.44e-09 ***
## Block332C              122138.8    20521.8   5.952 3.27e-09 ***
## Block333A              125827.1    20512.6   6.134 1.08e-09 ***
## Block333B              121768.0    22224.7   5.479 4.98e-08 ***
## Block333C              120881.5    20504.3   5.895 4.57e-09 ***
## Block333D              117240.4    20551.1   5.705 1.39e-08 ***
## Block334A              120703.4    19815.8   6.091 1.41e-09 ***
## Block334B              124089.2    19464.4   6.375 2.40e-10 ***
## Block334C              118697.9    22252.6   5.334 1.10e-07 ***
## Block335A              129809.5    19559.1   6.637 4.40e-11 ***
## Block335B              136287.1    24184.7   5.635 2.07e-08 ***
## Block335C              131160.9    19666.2   6.669 3.55e-11 ***
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## Block336B              127943.6    22282.9   5.742 1.12e-08 ***
## Block336C              121200.6    20161.8   6.011 2.28e-09 ***
## Block336D              140483.0    22165.9   6.338 3.04e-10 ***
## Block338A              137891.4    18330.7   7.522 9.00e-14 ***
## Block338B              125042.4    18412.7   6.791 1.57e-11 ***
## Block338C               97209.2    18033.0   5.391 8.09e-08 ***
## Block338D              154335.9    18560.9   8.315  < 2e-16 ***
## Block403A               46150.9    24177.6   1.909 0.056466 .  
## Block403B               47889.4    20484.5   2.338 0.019521 *  
## Block403C               34898.4    29151.4   1.197 0.231431    
## Block403D                7335.7    24422.2   0.300 0.763933    
## Block404A               45676.1    24176.5   1.889 0.059039 .  
## Block404B              -29924.4    22083.2  -1.355 0.175588    
## Block405B                3739.0    24148.5   0.155 0.876974    
## Block405C               58845.7    22176.8   2.653 0.008047 ** 
## Block406A                8367.1    29586.9   0.283 0.777370    
## Block406B               22057.1    24584.2   0.897 0.369745    
## Block406C               13081.2    22668.7   0.577 0.563981    
## Block407A               51492.7    20422.4   2.521 0.011788 *  
## Block407B               61675.3    24662.2   2.501 0.012492 *  
## Block408A               39962.3    20053.1   1.993 0.046453 *  
## Block408B               60877.3    20817.1   2.924 0.003501 ** 
## Block408C               55835.6    18868.6   2.959 0.003131 ** 
## Block409A               20932.7    18502.9   1.131 0.258092    
## Block409B               33710.4    23937.1   1.408 0.159242    
## Block410A               85890.4    19635.7   4.374 1.30e-05 ***
## Block410C               74856.0    21813.9   3.432 0.000616 ***
## Block411A               71533.1    29011.6   2.466 0.013782 *  
## Block411B               86257.0    20766.0   4.154 3.45e-05 ***
## Block412A               68570.7    23917.5   2.867 0.004200 ** 
## Block412B               39335.7    21854.0   1.800 0.072063 .  
## Block413A               27262.3    23817.0   1.145 0.252525    
## Block414A               91399.1    19884.7   4.596 4.64e-06 ***
## Block414B               89539.9    19676.1   4.551 5.76e-06 ***
## Block415A              133746.8    20328.2   6.579 6.42e-11 ***
## Block415B              151577.4    20961.1   7.231 7.44e-13 ***
## Block415C              132497.2    19107.5   6.934 5.94e-12 ***
## Block416A              101299.1    19072.6   5.311 1.24e-07 ***
## Block416B              121670.5    20991.9   5.796 8.19e-09 ***
## Block416C              114519.4    19878.6   5.761 1.00e-08 ***
## Block417A              140988.3    18005.4   7.830 8.88e-15 ***
## Block418A              100052.2    18625.4   5.372 8.96e-08 ***
## Block418B              118447.0    18349.1   6.455 1.44e-10 ***
## Block418C              120181.6    19140.8   6.279 4.40e-10 ***
## Block430A               48485.4    21153.4   2.292 0.022032 *  
## Block430B               78184.0    19806.5   3.947 8.25e-05 ***
## Block430C               68255.8    20586.3   3.316 0.000935 ***
## Block430D               73027.4    19515.6   3.742 0.000189 ***
## Block432A               70221.7    20518.6   3.422 0.000637 ***
## Block432B               69794.5    21089.9   3.309 0.000956 ***
## Block433A               77924.0    24340.6   3.201 0.001395 ** 
## Block433B               88289.5    19546.3   4.517 6.74e-06 ***
## Block434A              102247.4    22059.5   4.635 3.86e-06 ***
## Block434B               99047.3    19509.1   5.077 4.29e-07 ***
## Block435A               96028.6    20330.5   4.723 2.53e-06 ***
## Block435B              102469.4    20039.8   5.113 3.55e-07 ***
## Block435C              105553.0    24064.3   4.386 1.23e-05 ***
## Block436A               68071.8    23561.6   2.889 0.003916 ** 
## Block436B               66890.7    20528.4   3.258 0.001144 ** 
## Block436C               87314.3    18359.9   4.756 2.16e-06 ***
## Block438A               79871.4    21857.1   3.654 0.000266 ***
## Block438B               70109.7    21899.6   3.201 0.001395 ** 
## Block439A               93779.7    23852.3   3.932 8.80e-05 ***
## Block439B               70237.2    21866.3   3.212 0.001344 ** 
## Block439C               95939.7    29090.8   3.298 0.000996 ***
## Block440A               86236.5    20402.4   4.227 2.51e-05 ***
## Block440B               92666.9    19388.8   4.779 1.92e-06 ***
## Block440C               75951.5    24125.8   3.148 0.001674 ** 
## Block441A               92772.9    24038.4   3.859 0.000118 ***
## Block441B               80811.1    21985.2   3.676 0.000245 ***
## Block441C               94839.7    21943.9   4.322 1.64e-05 ***
## Block441D              126292.8    29139.5   4.334 1.56e-05 ***
## Block443A               76683.7    20764.7   3.693 0.000229 ***
## Block443B               87873.8    20188.7   4.353 1.43e-05 ***
## Block443C               79264.9    20786.2   3.813 0.000142 ***
## Block445A               94507.1    22010.3   4.294 1.86e-05 ***
## Block445B               78130.0    18992.9   4.114 4.10e-05 ***
## Block446B               69581.7    20336.3   3.422 0.000639 ***
## Block446C               44235.6    29152.6   1.517 0.129372    
## Block447A               80160.3    20937.5   3.829 0.000134 ***
## Block448A               75105.9    20117.7   3.733 0.000196 ***
## Block448B               93346.2    24339.9   3.835 0.000130 ***
## Block450A               61424.4    21202.4   2.897 0.003819 ** 
## Block450B              100362.5    22328.7   4.495 7.47e-06 ***
## Block451A               63258.2    20698.6   3.056 0.002280 ** 
## Block451B               72644.6    20579.2   3.530 0.000428 ***
## Block452A               79294.6    20580.5   3.853 0.000121 ***
## Block452B               83249.5    22365.6   3.722 0.000204 ***
## Block453A               78322.1    22368.5   3.501 0.000476 ***
## Block453B               81136.6    19819.0   4.094 4.46e-05 ***
## Block453C               76924.2    20669.9   3.722 0.000205 ***
## Block453D               92619.5    20667.1   4.481 7.95e-06 ***
## Block467A               79423.8    19308.9   4.113 4.10e-05 ***
## Block467B               75099.4    18584.0   4.041 5.58e-05 ***
## Block468A               74231.5    19371.2   3.832 0.000132 ***
## Block468B               90046.0    22038.9   4.086 4.61e-05 ***
## Block468C               82243.0    19146.4   4.295 1.85e-05 ***
## Block469A               74711.4    29110.0   2.567 0.010364 *  
## Block469B               88704.0    20321.3   4.365 1.35e-05 ***
## Block469C               73856.1    19307.1   3.825 0.000136 ***
## Block470A               71882.5    18557.6   3.873 0.000112 ***
## Block470B               79763.1    19899.7   4.008 6.40e-05 ***
## Block470C               68586.4    19105.7   3.590 0.000341 ***
## Block471A               83722.1    20403.2   4.103 4.28e-05 ***
## Block471B               80070.9    21020.6   3.809 0.000145 ***
## Block471C               87988.8    20985.2   4.193 2.91e-05 ***
## Block472A              111147.5    20322.5   5.469 5.25e-08 ***
## Block472B               89902.6    20407.9   4.405 1.13e-05 ***
## Block472C              100145.3    19101.1   5.243 1.80e-07 ***
## Block473A               93908.1    29718.0   3.160 0.001608 ** 
## years_used                   NA         NA      NA       NA    
## subzoneCompassvale           NA         NA      NA       NA    
## subzoneFernvale              NA         NA      NA       NA    
## subzoneRivervale             NA         NA      NA       NA    
## Story04 TO 06           26312.9     2131.9  12.342  < 2e-16 ***
## Story07 TO 09           46673.6     2085.4  22.381  < 2e-16 ***
## Story10 TO 12           51697.7     2153.0  24.012  < 2e-16 ***
## Story13 TO 15           59526.1     2077.3  28.656  < 2e-16 ***
## Story16 TO 18           72345.8     2615.8  27.658  < 2e-16 ***
## Story19 TO 21           67441.6     3790.2  17.794  < 2e-16 ***
## Story22 TO 24           76668.2     4256.8  18.011  < 2e-16 ***
## Story25 TO 27           77270.0     5886.0  13.128  < 2e-16 ***
## Area                     2717.3      716.2   3.794 0.000154 ***
## ModelModel A            13380.1     3093.3   4.326 1.62e-05 ***
## ModelModel A2                NA         NA      NA       NA    
## ModelPremium Apartment       NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 23180 on 1572 degrees of freedom
## Multiple R-squared:  0.9462, Adjusted R-squared:  0.9277 
## F-statistic: 50.96 on 543 and 1572 DF,  p-value: < 2.2e-16

Removing subzone

L3 <- lm(ResalePrice ~ .-subzone, 
         data = df)
summary(L3)
## 
## Call:
## lm(formula = ResalePrice ~ . - subzone, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -108099  -10797       0   11327   83503 
## 
## Coefficients: (31 not defined because of singularities)
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              57717.8    56921.9   1.014 0.310747    
## Date2022-02-01            3205.0     2814.8   1.139 0.255040    
## Date2022-03-01            6466.2     2705.6   2.390 0.016970 *  
## Date2022-04-01           17158.8     2692.6   6.373 2.44e-10 ***
## Date2022-05-01           18814.9     2712.3   6.937 5.84e-12 ***
## Date2022-06-01           25490.1     2826.4   9.018  < 2e-16 ***
## Date2022-07-01           28758.1     2614.3  11.000  < 2e-16 ***
## Date2022-08-01           31702.8     2674.3  11.855  < 2e-16 ***
## Date2022-09-01           40950.6     2693.9  15.201  < 2e-16 ***
## Date2022-10-01           45604.4     2955.5  15.430  < 2e-16 ***
## Date2022-11-01           52303.1     2884.9  18.130  < 2e-16 ***
## Date2022-12-01           53873.6     2829.7  19.039  < 2e-16 ***
## Type4 ROOM               44773.9    18376.4   2.436 0.014941 *  
## Type5 ROOM              109528.5    32417.7   3.379 0.000746 ***
## Block104                 38496.4    28571.1   1.347 0.178050    
## Block105                 29117.8    20223.1   1.440 0.150115    
## Block106                 12158.8    21354.2   0.569 0.569176    
## Block107                 20476.7    19467.4   1.052 0.293034    
## Block108                 22050.0    23269.1   0.948 0.343474    
## Block109                 -5928.6    19034.0  -0.311 0.755482    
## Block112                 36912.5    28595.6   1.291 0.196946    
## Block113                  9837.5    28592.5   0.344 0.730847    
## Block114                 23623.2    23352.6   1.012 0.311891    
## Block115                 -3738.4    21281.9  -0.176 0.860583    
## Block116A                 7067.1    23750.3   0.298 0.766082    
## Block116B                15253.1    28877.6   0.528 0.597437    
## Block116C                19600.5    23678.2   0.828 0.407918    
## Block117A                30498.8    28900.2   1.055 0.291444    
## Block117B                 6985.0    28797.4   0.243 0.808381    
## Block117C                -8221.0    21710.6  -0.379 0.704988    
## Block119A                76515.9    28645.3   2.671 0.007637 ** 
## Block119D                39860.5    28698.0   1.389 0.165040    
## Block120A                41046.0    28708.4   1.430 0.152986    
## Block120B                49664.9    28669.6   1.732 0.083413 .  
## Block121                 -3589.3    20243.1  -0.177 0.859287    
## Block121A                 2548.2    21621.5   0.118 0.906198    
## Block121C                  218.0    21571.1   0.010 0.991938    
## Block121D                -2607.4    21057.2  -0.124 0.901472    
## Block122                -17958.3    21572.7  -0.832 0.405280    
## Block122A                -5613.1    20845.0  -0.269 0.787750    
## Block122D                -8490.3    29604.6  -0.287 0.774312    
## Block122E               -18036.5    21132.1  -0.854 0.393506    
## Block123                -12474.1    19622.4  -0.636 0.525060    
## Block123A                23734.7    28569.0   0.831 0.406221    
## Block123B               -23287.1    20364.5  -1.144 0.252998    
## Block123C                -8667.4    28693.4  -0.302 0.762640    
## Block123D               -16957.1    23692.2  -0.716 0.474268    
## Block123E               -41107.1    28840.9  -1.425 0.154267    
## Block124                   806.2    23300.2   0.035 0.972401    
## Block124A                  175.7    19451.8   0.009 0.992794    
## Block124B                52519.1    22812.8   2.302 0.021455 *  
## Block124C                35324.0    22788.4   1.550 0.121323    
## Block125                -11127.2    20107.0  -0.553 0.580069    
## Block126                 10652.7    23343.7   0.456 0.648207    
## Block128                 -7316.3    20149.9  -0.363 0.716583    
## Block129                -20893.8    28547.0  -0.732 0.464333    
## Block131                 36484.8    24171.7   1.509 0.131398    
## Block132                 -9076.1    19508.1  -0.465 0.641818    
## Block133                -18675.4    20151.6  -0.927 0.354201    
## Block134                 -7830.2    21296.6  -0.368 0.713167    
## Block140                 13519.9    29420.2   0.460 0.645907    
## Block141                 -6702.0    21264.9  -0.315 0.752676    
## Block142                -35326.5    23351.0  -1.513 0.130520    
## Block145                 12061.7    28564.9   0.422 0.672897    
## Block146                -21015.1    28571.8  -0.736 0.462134    
## Block148                 -9783.0    21351.5  -0.458 0.646882    
## Block150                 34188.8    24566.5   1.392 0.164214    
## Block151                 16700.0    20909.6   0.799 0.424598    
## Block152                 17609.9    22641.8   0.778 0.436829    
## Block153                 41538.5    21584.6   1.924 0.054478 .  
## Block154                 39028.0    29534.1   1.321 0.186541    
## Block155                 22715.0    24612.2   0.923 0.356193    
## Block156                 40167.4    22615.3   1.776 0.075908 .  
## Block157A                  109.1    19773.7   0.006 0.995599    
## Block157B                45583.9    20930.1   2.178 0.029561 *  
## Block157C                 3749.8    24503.7   0.153 0.878396    
## Block157D                11478.4    21209.9   0.541 0.588458    
## Block158A                -2289.1    21490.5  -0.107 0.915184    
## Block158B               -23123.0    24311.6  -0.951 0.341695    
## Block158C                -5475.9    20581.2  -0.266 0.790225    
## Block158D                26833.8    24024.4   1.117 0.264191    
## Block159A                34076.8    21541.9   1.582 0.113878    
## Block162A                87940.9    19513.4   4.507 7.07e-06 ***
## Block162B                77576.7    19889.7   3.900 0.000100 ***
## Block162C                70866.9    20276.7   3.495 0.000487 ***
## Block163A                69773.3    19530.6   3.573 0.000364 ***
## Block163B                95744.0    21997.4   4.353 1.43e-05 ***
## Block163C                69544.6    22080.1   3.150 0.001665 ** 
## Block164A                73225.1    19837.1   3.691 0.000231 ***
## Block164B                89201.0    20390.9   4.375 1.30e-05 ***
## Block164C                73540.3    20320.6   3.619 0.000305 ***
## Block178A                56712.7    22036.5   2.574 0.010156 *  
## Block178B                35053.8    19306.2   1.816 0.069612 .  
## Block178C                59347.9    19574.9   3.032 0.002470 ** 
## Block178D                33431.1    29125.0   1.148 0.251207    
## Block180A                75002.5    24250.5   3.093 0.002017 ** 
## Block180B                88954.2    20672.0   4.303 1.79e-05 ***
## Block180C                39599.1    19317.5   2.050 0.040540 *  
## Block180D                76942.2    20669.3   3.723 0.000204 ***
## Block183A               -24440.3    21031.2  -1.162 0.245372    
## Block183B                22273.0    29643.8   0.751 0.452553    
## Block183C               -19923.7    21659.4  -0.920 0.357785    
## Block183D                33717.7    22445.2   1.502 0.133241    
## Block184A                -3530.9    24580.2  -0.144 0.885797    
## Block184B               -31621.2    29588.1  -1.069 0.285363    
## Block184C                32988.9    24264.9   1.360 0.174173    
## Block185A                 3642.2    24588.9   0.148 0.882264    
## Block185B                24153.1    24335.8   0.992 0.321110    
## Block185C                39713.5    23522.7   1.688 0.091550 .  
## Block185D                40387.3    22196.8   1.820 0.069024 .  
## Block186A               -28361.0    24688.9  -1.149 0.250840    
## Block186B               -29657.2    21605.3  -1.373 0.170047    
## Block186C                 7396.4    21625.4   0.342 0.732378    
## Block186D                 1727.3    29451.9   0.059 0.953238    
## Block187B               -38745.3    24554.3  -1.578 0.114781    
## Block188B                -5514.7    20500.3  -0.269 0.787961    
## Block188C               -47426.3    23695.6  -2.001 0.045512 *  
## Block188D               -33069.0    20599.9  -1.605 0.108629    
## Block190A                 -399.3    23603.2  -0.017 0.986505    
## Block190B                14717.0    21687.4   0.679 0.497493    
## Block191B                -9600.5    23755.2  -0.404 0.686162    
## Block192A                45345.8    23652.7   1.917 0.055400 .  
## Block192B               -15033.9    28878.8  -0.521 0.602730    
## Block192C                -6398.5    23709.4  -0.270 0.787294    
## Block193                 -2958.7    20758.4  -0.143 0.886680    
## Block194                  3513.8    21429.9   0.164 0.869777    
## Block195                 14105.4    24403.9   0.578 0.563348    
## Block196                 -6875.3    21408.4  -0.321 0.748141    
## Block197                 -2528.8    20278.0  -0.125 0.900771    
## Block200A                30078.5    21002.0   1.432 0.152293    
## Block200B                20152.7    29601.7   0.681 0.496101    
## Block201A                15479.2    29578.4   0.523 0.600820    
## Block201B                49480.2    22692.8   2.180 0.029373 *  
## Block201C                41883.3    24581.8   1.704 0.088610 .  
## Block201D                29470.9    22668.4   1.300 0.193761    
## Block202                 52459.3    26165.4   2.005 0.045143 *  
## Block202C                43756.9    22659.9   1.931 0.053659 .  
## Block203B                40384.1    24615.6   1.641 0.101082    
## Block203C                28477.3    22634.2   1.258 0.208523    
## Block203E                20204.1    22674.4   0.891 0.373037    
## Block204A                27431.9    24587.3   1.116 0.264724    
## Block204B                33889.0    22613.8   1.499 0.134179    
## Block204C                19192.8    29617.7   0.648 0.517069    
## Block205C                 -368.4    21299.2  -0.017 0.986202    
## Block206A                 3084.5    28582.0   0.108 0.914075    
## Block206B                 3848.8    20257.6   0.190 0.849338    
## Block206C                 5277.5    20230.9   0.261 0.794232    
## Block206D                 4953.2    23303.6   0.213 0.831704    
## Block207A                29971.6    24190.9   1.239 0.215546    
## Block207B                32955.7    22492.2   1.465 0.143065    
## Block207C                 3669.0    29543.6   0.124 0.901180    
## Block207D                47514.0    24939.3   1.905 0.056938 .  
## Block208A               100577.7    22259.2   4.518 6.69e-06 ***
## Block208B                89075.1    20513.5   4.342 1.50e-05 ***
## Block209A                75695.8    21181.3   3.574 0.000363 ***
## Block209B                92043.3    24337.7   3.782 0.000161 ***
## Block209C               100094.7    21253.0   4.710 2.70e-06 ***
## Block210A                87386.0    19277.1   4.533 6.25e-06 ***
## Block210B                83437.9    20286.6   4.113 4.11e-05 ***
## Block210C                92157.7    22033.3   4.183 3.04e-05 ***
## Block211A               101753.5    19789.7   5.142 3.06e-07 ***
## Block211B                86253.1    21007.4   4.106 4.24e-05 ***
## Block211C                92884.4    18524.5   5.014 5.93e-07 ***
## Block211D                88759.2    19185.3   4.626 4.03e-06 ***
## Block212A                77728.5    21815.1   3.563 0.000377 ***
## Block212B               108366.8    21487.0   5.043 5.10e-07 ***
## Block212C                89459.2    21932.8   4.079 4.75e-05 ***
## Block213A                95698.5    21546.5   4.441 9.56e-06 ***
## Block213B                79311.0    19570.5   4.053 5.31e-05 ***
## Block215A               199889.4    19315.6  10.349  < 2e-16 ***
## Block215B               234050.4    19826.9  11.805  < 2e-16 ***
## Block216A               269243.0    20613.6  13.061  < 2e-16 ***
## Block216B               282925.9    19564.6  14.461  < 2e-16 ***
## Block216C               275487.4    24250.6  11.360  < 2e-16 ***
## Block216D               241195.5    19847.1  12.153  < 2e-16 ***
## Block217A               234767.4    20672.5  11.356  < 2e-16 ***
## Block217B               186543.6    20642.6   9.037  < 2e-16 ***
## Block217C               259604.7    20147.2  12.885  < 2e-16 ***
## Block223B                24989.0    28548.9   0.875 0.381541    
## Block223C                10375.1    23342.5   0.444 0.656764    
## Block223D                42521.6    21281.5   1.998 0.045882 *  
## Block224B                29394.8    21289.8   1.381 0.167567    
## Block224C                42861.8    28465.3   1.506 0.132331    
## Block224D                40313.0    21340.8   1.889 0.059074 .  
## Block225A                15231.9    28542.1   0.534 0.593649    
## Block225B                 4901.4    21484.1   0.228 0.819566    
## Block226A                -6867.8    28554.7  -0.241 0.809963    
## Block226B                20008.0    21337.9   0.938 0.348555    
## Block227A                50265.3    28584.6   1.758 0.078862 .  
## Block227C                -2237.6    21365.9  -0.105 0.916606    
## Block227D                25589.3    28529.8   0.897 0.369892    
## Block228A               -18834.6    23720.6  -0.794 0.427303    
## Block228B                33269.3    19493.3   1.707 0.088075 .  
## Block228C                -9427.9    23725.2  -0.397 0.691142    
## Block229                -10554.5    21322.0  -0.495 0.620665    
## Block230                  2938.9    21250.7   0.138 0.890024    
## Block231                 33247.5    23315.3   1.426 0.154069    
## Block232                 18873.9    23320.6   0.809 0.418452    
## Block235                 36243.2    23349.7   1.552 0.120817    
## Block236                  2548.1    21366.6   0.119 0.905087    
## Block237                 24801.1    20206.9   1.227 0.219873    
## Block238                 30008.9    20172.3   1.488 0.137049    
## Block239                 38828.8    28571.8   1.359 0.174344    
## Block240                 34253.7    28464.4   1.203 0.229009    
## Block241                 22964.2    28506.8   0.806 0.420612    
## Block244                 -8385.0    23577.0  -0.356 0.722154    
## Block245                 -7455.3    23577.2  -0.316 0.751887    
## Block246                 55294.1    21610.0   2.559 0.010598 *  
## Block247                 82054.6    25412.6   3.229 0.001268 ** 
## Block248                  5634.6    28793.6   0.196 0.844878    
## Block251                -29353.6    23627.2  -1.242 0.214288    
## Block253                -13889.5    28870.8  -0.481 0.630518    
## Block255                -16464.3    21562.8  -0.764 0.445248    
## Block257A                39037.7    24587.5   1.588 0.112554    
## Block257B               126430.6    25415.1   4.975 7.25e-07 ***
## Block257C                58627.5    24542.1   2.389 0.017018 *  
## Block258A                67939.0    22658.4   2.998 0.002757 ** 
## Block258B                60081.1    22684.0   2.649 0.008163 ** 
## Block258C                41140.1    21630.0   1.902 0.057355 .  
## Block258D                50711.5    21017.0   2.413 0.015941 *  
## Block259A                40514.5    29613.5   1.368 0.171473    
## Block259B                71186.1    26150.2   2.722 0.006556 ** 
## Block259C                39999.0    29599.1   1.351 0.176774    
## Block260A               106882.8    22647.9   4.719 2.58e-06 ***
## Block260B               101399.7    29541.7   3.432 0.000614 ***
## Block260C                54778.8    21666.5   2.528 0.011560 *  
## Block260D               110941.5    24578.0   4.514 6.84e-06 ***
## Block261A                57022.0    21642.2   2.635 0.008502 ** 
## Block261B                63865.8    24553.9   2.601 0.009381 ** 
## Block261C               132499.4    29707.3   4.460 8.77e-06 ***
## Block262A                38339.6    20560.2   1.865 0.062403 .  
## Block262D                18712.2    24585.1   0.761 0.446699    
## Block264A               115974.3    24367.7   4.759 2.12e-06 ***
## Block264B               141542.2    24367.1   5.809 7.60e-09 ***
## Block264C               162392.9    29428.5   5.518 4.00e-08 ***
## Block264D               170407.9    29420.2   5.792 8.37e-09 ***
## Block264E               155671.0    24333.9   6.397 2.08e-10 ***
## Block264F               176973.6    29322.9   6.035 1.97e-09 ***
## Block265A               200390.2    29428.8   6.809 1.39e-11 ***
## Block265B               147994.6    29409.7   5.032 5.41e-07 ***
## Block265C               121753.4    21397.3   5.690 1.51e-08 ***
## Block265D               157795.0    20278.5   7.781 1.29e-14 ***
## Block266A               155337.6    21406.3   7.257 6.21e-13 ***
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## Block278C               186153.0    21174.4   8.791  < 2e-16 ***
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## Block279B               265811.3    20562.4  12.927  < 2e-16 ***
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## Block281B               221507.1    20732.3  10.684  < 2e-16 ***
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## Block282C               265148.3    19527.1  13.578  < 2e-16 ***
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## Block288C               135862.4    18347.2   7.405 2.13e-13 ***
## Block289A               157307.3    18037.4   8.721  < 2e-16 ***
## Block289B               140295.3    18298.0   7.667 3.06e-14 ***
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## Block290B                 2960.5    21606.2   0.137 0.891033    
## Block290C               -11680.4    24549.4  -0.476 0.634287    
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## Block293A               127150.0    18907.7   6.725 2.45e-11 ***
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## Block293D               133481.4    19508.9   6.842 1.11e-11 ***
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## Block295B               -25933.5    21011.9  -1.234 0.217302    
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## Block296A                -2695.9    22691.2  -0.119 0.905444    
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## Block298A                 9256.4    19536.0   0.474 0.635699    
## Block298B                42330.9    22016.3   1.923 0.054697 .  
## Block298C                11613.6    21932.6   0.530 0.596524    
## Block298D                  466.0    19402.0   0.024 0.980842    
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## Block301C               -10065.4    22651.4  -0.444 0.656842    
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## Block302A                 -457.4    29604.6  -0.015 0.987675    
## Block302B                57185.7    21322.2   2.682 0.007395 ** 
## Block303A                 6393.3    24577.1   0.260 0.794796    
## Block303B                55995.8    22488.0   2.490 0.012876 *  
## Block303C                50962.8    23341.3   2.183 0.029156 *  
## Block304A                21252.5    22691.7   0.937 0.349121    
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## Block307C                 5968.4    24521.1   0.243 0.807729    
## Block308A               -18656.1    29543.7  -0.631 0.527821    
## Block308B                  818.6    22675.7   0.036 0.971207    
## Block308C                -7924.9    20554.3  -0.386 0.699876    
## Block309A                60081.7    29694.0   2.023 0.043205 *  
## Block309B                23973.5    20581.1   1.165 0.244263    
## Block309C                49900.9    24203.6   2.062 0.039399 *  
## Block309D                39364.9    21099.3   1.866 0.062270 .  
## Block310B                 6635.3    24387.9   0.272 0.785601    
## Block311A                10328.2    20000.7   0.516 0.605653    
## Block311B                 8107.2    24446.4   0.332 0.740213    
## Block311C                  499.0    21298.1   0.023 0.981310    
## Block311D                31909.3    21356.2   1.494 0.135337    
## Block312A               -56128.6    29074.3  -1.931 0.053722 .  
## Block312B               -18861.7    29426.6  -0.641 0.521633    
## Block313A                 1577.5    29587.7   0.053 0.957486    
## Block313B               -20841.5    24585.4  -0.848 0.396723    
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## Block314C                16152.7    29601.7   0.546 0.585371    
## Block314D                72049.0    29394.5   2.451 0.014350 *  
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## Block315B                17542.6    29604.6   0.593 0.553559    
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## Block317B                -1784.5    24430.4  -0.073 0.941779    
## Block317C                46973.6    29322.9   1.602 0.109369    
## Block317D                61131.2    24363.1   2.509 0.012201 *  
## Block318A                84576.4    29376.7   2.879 0.004043 ** 
## Block318B                 7982.9    22646.6   0.352 0.724511    
## Block318C                 9982.0    29530.1   0.338 0.735388    
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## Block319B                14202.9    24488.9   0.580 0.562016    
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## Block320A                79278.0    30912.1   2.565 0.010421 *  
## Block320B                20875.5    24572.2   0.850 0.395701    
## Block320D                69982.0    29530.1   2.370 0.017915 *  
## Block321A                38531.0    24570.4   1.568 0.117038    
## Block321B                42082.3    22678.2   1.856 0.063694 .  
## Block321C                35480.3    22648.5   1.567 0.117418    
## Block322A                62596.4    25824.5   2.424 0.015467 *  
## Block322B                47201.1    20944.0   2.254 0.024353 *  
## Block323B                56746.5    20251.7   2.802 0.005140 ** 
## Block323C                67112.5    24594.1   2.729 0.006427 ** 
## Block324A                86765.8    25423.3   3.413 0.000659 ***
## Block324B                81855.0    24632.8   3.323 0.000911 ***
## Block324D                79382.8    24593.9   3.228 0.001273 ** 
## Block325A                46143.8    21305.0   2.166 0.030471 *  
## Block325B                41046.7    20972.9   1.957 0.050509 .  
## Block325C                32346.6    21627.3   1.496 0.134949    
## Block326A               139137.4    21254.4   6.546 7.96e-11 ***
## Block326B               124744.9    20546.6   6.071 1.59e-09 ***
## Block326C               124992.3    19360.3   6.456 1.43e-10 ***
## Block326D               136322.6    21290.5   6.403 2.01e-10 ***
## Block327A                89144.4    29396.6   3.032 0.002465 ** 
## Block327C               108826.6    22445.0   4.849 1.37e-06 ***
## Block329A                96103.2    20469.0   4.695 2.90e-06 ***
## Block329B               106132.6    22055.0   4.812 1.64e-06 ***
## Block330A               105958.9    19654.8   5.391 8.07e-08 ***
## Block330B               118340.8    20396.1   5.802 7.90e-09 ***
## Block331A               101937.0    18659.7   5.463 5.44e-08 ***
## Block331B               152420.2    29262.2   5.209 2.15e-07 ***
## Block331C               100060.5    21202.6   4.719 2.58e-06 ***
## Block332A               115476.7    21171.6   5.454 5.70e-08 ***
## Block332B               118638.4    19487.8   6.088 1.44e-09 ***
## Block332C               122138.8    20521.8   5.952 3.27e-09 ***
## Block333A               125827.1    20512.6   6.134 1.08e-09 ***
## Block333B               121768.0    22224.7   5.479 4.98e-08 ***
## Block333C               120881.5    20504.3   5.895 4.57e-09 ***
## Block333D               117240.4    20551.1   5.705 1.39e-08 ***
## Block334A               120703.4    19815.8   6.091 1.41e-09 ***
## Block334B               124089.2    19464.4   6.375 2.40e-10 ***
## Block334C               118697.9    22252.6   5.334 1.10e-07 ***
## Block335A               129809.5    19559.1   6.637 4.40e-11 ***
## Block335B               136287.1    24184.7   5.635 2.07e-08 ***
## Block335C               131160.9    19666.2   6.669 3.55e-11 ***
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## Block336B               127943.6    22282.9   5.742 1.12e-08 ***
## Block336C               121200.6    20161.8   6.011 2.28e-09 ***
## Block336D               140483.0    22165.9   6.338 3.04e-10 ***
## Block338A               137891.4    18330.7   7.522 9.00e-14 ***
## Block338B               125042.4    18412.7   6.791 1.57e-11 ***
## Block338C                97209.2    18033.0   5.391 8.09e-08 ***
## Block338D               154335.9    18560.9   8.315  < 2e-16 ***
## Block403A                46150.9    24177.6   1.909 0.056466 .  
## Block403B                47889.4    20484.5   2.338 0.019521 *  
## Block403C                34898.4    29151.4   1.197 0.231431    
## Block403D                 7335.7    24422.2   0.300 0.763933    
## Block404A                45676.1    24176.5   1.889 0.059039 .  
## Block404B               -29924.4    22083.2  -1.355 0.175588    
## Block405B                 3739.0    24148.5   0.155 0.876974    
## Block405C                58845.7    22176.8   2.653 0.008047 ** 
## Block406A                 8367.1    29586.9   0.283 0.777370    
## Block406B                22057.1    24584.2   0.897 0.369745    
## Block406C                13081.2    22668.7   0.577 0.563981    
## Block407A                51492.7    20422.4   2.521 0.011788 *  
## Block407B                61675.3    24662.2   2.501 0.012492 *  
## Block408A                39962.3    20053.1   1.993 0.046453 *  
## Block408B                60877.3    20817.1   2.924 0.003501 ** 
## Block408C                55835.6    18868.6   2.959 0.003131 ** 
## Block409A                20932.7    18502.9   1.131 0.258092    
## Block409B                33710.4    23937.1   1.408 0.159242    
## Block410A                85890.4    19635.7   4.374 1.30e-05 ***
## Block410C                74856.0    21813.9   3.432 0.000616 ***
## Block411A                71533.1    29011.6   2.466 0.013782 *  
## Block411B                86257.0    20766.0   4.154 3.45e-05 ***
## Block412A                68570.7    23917.5   2.867 0.004200 ** 
## Block412B                39335.7    21854.0   1.800 0.072063 .  
## Block413A                27262.3    23817.0   1.145 0.252525    
## Block414A                91399.1    19884.7   4.596 4.64e-06 ***
## Block414B                89539.9    19676.1   4.551 5.76e-06 ***
## Block415A               133746.8    20328.2   6.579 6.42e-11 ***
## Block415B               151577.4    20961.1   7.231 7.44e-13 ***
## Block415C               132497.2    19107.5   6.934 5.94e-12 ***
## Block416A               101299.1    19072.6   5.311 1.24e-07 ***
## Block416B               121670.5    20991.9   5.796 8.19e-09 ***
## Block416C               114519.4    19878.6   5.761 1.00e-08 ***
## Block417A               140988.3    18005.4   7.830 8.88e-15 ***
## Block418A               100052.2    18625.4   5.372 8.96e-08 ***
## Block418B               118447.0    18349.1   6.455 1.44e-10 ***
## Block418C               120181.6    19140.8   6.279 4.40e-10 ***
## Block430A                48485.4    21153.4   2.292 0.022032 *  
## Block430B                78184.0    19806.5   3.947 8.25e-05 ***
## Block430C                68255.8    20586.3   3.316 0.000935 ***
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## Block432B                69794.5    21089.9   3.309 0.000956 ***
## Block433A                77924.0    24340.6   3.201 0.001395 ** 
## Block433B                88289.5    19546.3   4.517 6.74e-06 ***
## Block434A               102247.4    22059.5   4.635 3.86e-06 ***
## Block434B                99047.3    19509.1   5.077 4.29e-07 ***
## Block435A                96028.6    20330.5   4.723 2.53e-06 ***
## Block435B               102469.4    20039.8   5.113 3.55e-07 ***
## Block435C               105553.0    24064.3   4.386 1.23e-05 ***
## Block436A                68071.8    23561.6   2.889 0.003916 ** 
## Block436B                66890.7    20528.4   3.258 0.001144 ** 
## Block436C                87314.3    18359.9   4.756 2.16e-06 ***
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## Block438B                70109.7    21899.6   3.201 0.001395 ** 
## Block439A                93779.7    23852.3   3.932 8.80e-05 ***
## Block439B                70237.2    21866.3   3.212 0.001344 ** 
## Block439C                95939.7    29090.8   3.298 0.000996 ***
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## Block440B                92666.9    19388.8   4.779 1.92e-06 ***
## Block440C                75951.5    24125.8   3.148 0.001674 ** 
## Block441A                92772.9    24038.4   3.859 0.000118 ***
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## Block443B                87873.8    20188.7   4.353 1.43e-05 ***
## Block443C                79264.9    20786.2   3.813 0.000142 ***
## Block445A                94507.1    22010.3   4.294 1.86e-05 ***
## Block445B                78130.0    18992.9   4.114 4.10e-05 ***
## Block446B                69581.7    20336.3   3.422 0.000639 ***
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## Block447A                80160.3    20937.5   3.829 0.000134 ***
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## Block448B                93346.2    24339.9   3.835 0.000130 ***
## Block450A                61424.4    21202.4   2.897 0.003819 ** 
## Block450B               100362.5    22328.7   4.495 7.47e-06 ***
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## Block451B                72644.6    20579.2   3.530 0.000428 ***
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## Block468C                82243.0    19146.4   4.295 1.85e-05 ***
## Block469A                74711.4    29110.0   2.567 0.010364 *  
## Block469B                88704.0    20321.3   4.365 1.35e-05 ***
## Block469C                73856.1    19307.1   3.825 0.000136 ***
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## Block470B                79763.1    19899.7   4.008 6.40e-05 ***
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## Block471B                80070.9    21020.6   3.809 0.000145 ***
## Block471C                87988.8    20985.2   4.193 2.91e-05 ***
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## Block472B                89902.6    20407.9   4.405 1.13e-05 ***
## Block472C               100145.3    19101.1   5.243 1.80e-07 ***
## Block473A                93908.1    29718.0   3.160 0.001608 ** 
## years_used                    NA         NA      NA       NA    
## StreetANCHORVALE DR           NA         NA      NA       NA    
## StreetANCHORVALE LANE         NA         NA      NA       NA    
## StreetANCHORVALE LINK         NA         NA      NA       NA    
## StreetANCHORVALE RD           NA         NA      NA       NA    
## StreetANCHORVALE ST           NA         NA      NA       NA    
## StreetCOMPASSVALE BOW         NA         NA      NA       NA    
## StreetCOMPASSVALE CRES        NA         NA      NA       NA    
## StreetCOMPASSVALE DR          NA         NA      NA       NA    
## StreetCOMPASSVALE LANE        NA         NA      NA       NA    
## StreetCOMPASSVALE LINK        NA         NA      NA       NA    
## StreetCOMPASSVALE RD          NA         NA      NA       NA    
## StreetCOMPASSVALE ST          NA         NA      NA       NA    
## StreetCOMPASSVALE WALK        NA         NA      NA       NA    
## StreetFERNVALE LANE           NA         NA      NA       NA    
## StreetFERNVALE LINK           NA         NA      NA       NA    
## StreetFERNVALE RD             NA         NA      NA       NA    
## StreetFERNVALE ST             NA         NA      NA       NA    
## StreetJLN KAYU                NA         NA      NA       NA    
## StreetRIVERVALE CRES          NA         NA      NA       NA    
## StreetRIVERVALE DR            NA         NA      NA       NA    
## StreetRIVERVALE ST            NA         NA      NA       NA    
## StreetRIVERVALE WALK          NA         NA      NA       NA    
## StreetSENGKANG CTRL           NA         NA      NA       NA    
## StreetSENGKANG EAST AVE       NA         NA      NA       NA    
## StreetSENGKANG EAST RD        NA         NA      NA       NA    
## StreetSENGKANG EAST WAY       NA         NA      NA       NA    
## StreetSENGKANG WEST AVE       NA         NA      NA       NA    
## StreetSENGKANG WEST WAY       NA         NA      NA       NA    
## Story04 TO 06            26312.9     2131.9  12.342  < 2e-16 ***
## Story07 TO 09            46673.6     2085.4  22.381  < 2e-16 ***
## Story10 TO 12            51697.7     2153.0  24.012  < 2e-16 ***
## Story13 TO 15            59526.1     2077.3  28.656  < 2e-16 ***
## Story16 TO 18            72345.8     2615.8  27.658  < 2e-16 ***
## Story19 TO 21            67441.6     3790.2  17.794  < 2e-16 ***
## Story22 TO 24            76668.2     4256.8  18.011  < 2e-16 ***
## Story25 TO 27            77270.0     5886.0  13.128  < 2e-16 ***
## Area                      2717.3      716.2   3.794 0.000154 ***
## ModelModel A             13380.1     3093.3   4.326 1.62e-05 ***
## ModelModel A2                 NA         NA      NA       NA    
## ModelPremium Apartment        NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 23180 on 1572 degrees of freedom
## Multiple R-squared:  0.9462, Adjusted R-squared:  0.9277 
## F-statistic: 50.96 on 543 and 1572 DF,  p-value: < 2.2e-16

It would seem removing Block would be the best. Now we will compare between street and subzone ## Removing Block and Street

L4 <- lm(ResalePrice ~ .-Block-Street, 
         data = df)
summary(L4)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - Street, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -111775  -25162   -3721   20006  172169 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            260974.1    21120.5  12.356  < 2e-16 ***
## Date2022-02-01           2414.2     4180.3   0.578 0.563656    
## Date2022-03-01           3931.7     4019.8   0.978 0.328142    
## Date2022-04-01          18956.2     3953.6   4.795 1.74e-06 ***
## Date2022-05-01          20446.6     4010.1   5.099 3.73e-07 ***
## Date2022-06-01          29936.2     4125.4   7.257 5.57e-13 ***
## Date2022-07-01          34120.7     3860.0   8.840  < 2e-16 ***
## Date2022-08-01          33073.6     3938.9   8.397  < 2e-16 ***
## Date2022-09-01          48602.3     3952.8  12.296  < 2e-16 ***
## Date2022-10-01          50222.4     4265.1  11.775  < 2e-16 ***
## Date2022-11-01          53405.2     4213.7  12.674  < 2e-16 ***
## Date2022-12-01          61225.8     4116.4  14.874  < 2e-16 ***
## Type4 ROOM              68329.9     8322.1   8.211 3.81e-16 ***
## Type5 ROOM             125283.1    14327.1   8.744  < 2e-16 ***
## years_used              -6846.1      145.7 -46.988  < 2e-16 ***
## subzoneCompassvale      33202.2     2458.4  13.506  < 2e-16 ***
## subzoneFernvale        -11416.8     2956.0  -3.862 0.000116 ***
## subzoneRivervale       -14757.9     2996.5  -4.925 9.10e-07 ***
## Story04 TO 06           22522.7     3088.3   7.293 4.28e-13 ***
## Story07 TO 09           40386.8     3056.0  13.215  < 2e-16 ***
## Story10 TO 12           49134.0     3157.5  15.561  < 2e-16 ***
## Story13 TO 15           53211.7     3049.4  17.450  < 2e-16 ***
## Story16 TO 18           66251.2     3809.6  17.391  < 2e-16 ***
## Story19 TO 21           62711.0     5686.6  11.028  < 2e-16 ***
## Story22 TO 24           67144.0     6397.2  10.496  < 2e-16 ***
## Story25 TO 27           60884.6     8888.7   6.850 9.71e-12 ***
## Area                     2151.6      306.2   7.026 2.86e-12 ***
## ModelModel A            -6370.3     3842.6  -1.658 0.097504 .  
## ModelModel A2           26486.9     6857.3   3.863 0.000116 ***
## ModelPremium Apartment  15687.1     3055.2   5.135 3.09e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 39150 on 2086 degrees of freedom
## Multiple R-squared:  0.7965, Adjusted R-squared:  0.7937 
## F-statistic: 281.5 on 29 and 2086 DF,  p-value: < 2.2e-16

Removing Block and subzone

L5 <- lm(ResalePrice ~ .-Block-subzone, data = df)
summary(L5)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - subzone, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -124088  -18948    -270   17004  129236 
## 
## Coefficients:
##                          Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             206911.59   23135.45   8.943  < 2e-16 ***
## Date2022-02-01            3338.51    3170.47   1.053 0.292463    
## Date2022-03-01           10296.40    3053.29   3.372 0.000759 ***
## Date2022-04-01           19656.14    2999.37   6.553 7.08e-11 ***
## Date2022-05-01           23350.74    3061.68   7.627 3.65e-14 ***
## Date2022-06-01           30759.13    3143.44   9.785  < 2e-16 ***
## Date2022-07-01           34567.35    2938.94  11.762  < 2e-16 ***
## Date2022-08-01           35800.25    3000.31  11.932  < 2e-16 ***
## Date2022-09-01           47473.78    3006.79  15.789  < 2e-16 ***
## Date2022-10-01           54249.69    3242.88  16.729  < 2e-16 ***
## Date2022-11-01           56095.57    3216.83  17.438  < 2e-16 ***
## Date2022-12-01           64365.55    3126.62  20.586  < 2e-16 ***
## Type4 ROOM               48466.79    8660.07   5.597 2.48e-08 ***
## Type5 ROOM              109702.71   15113.66   7.259 5.52e-13 ***
## years_used               -7945.05     172.76 -45.988  < 2e-16 ***
## StreetANCHORVALE DR      31976.16    6270.38   5.100 3.72e-07 ***
## StreetANCHORVALE LANE   -12063.89    7816.20  -1.543 0.122876    
## StreetANCHORVALE LINK    12337.10    4447.85   2.774 0.005592 ** 
## StreetANCHORVALE RD         38.32    4704.42   0.008 0.993501    
## StreetANCHORVALE ST       4975.65    5598.57   0.889 0.374249    
## StreetCOMPASSVALE BOW    91750.90    5010.71  18.311  < 2e-16 ***
## StreetCOMPASSVALE CRES    6066.40    3343.44   1.814 0.069759 .  
## StreetCOMPASSVALE DR     73433.80    4299.40  17.080  < 2e-16 ***
## StreetCOMPASSVALE LANE   10721.81    4382.79   2.446 0.014514 *  
## StreetCOMPASSVALE LINK  107434.40    5062.84  21.220  < 2e-16 ***
## StreetCOMPASSVALE RD     47502.05    5846.44   8.125 7.63e-16 ***
## StreetCOMPASSVALE ST      7914.06    5367.01   1.475 0.140480    
## StreetCOMPASSVALE WALK   44132.34    6462.40   6.829 1.12e-11 ***
## StreetFERNVALE LANE      -7399.87    7597.29  -0.974 0.330164    
## StreetFERNVALE LINK     -10920.43    3551.25  -3.075 0.002132 ** 
## StreetFERNVALE RD          926.48    3979.00   0.233 0.815907    
## StreetFERNVALE ST       -12788.23    5996.82  -2.133 0.033083 *  
## StreetJLN KAYU          -12961.66    9887.74  -1.311 0.190044    
## StreetRIVERVALE CRES    -23855.90    3758.86  -6.347 2.70e-10 ***
## StreetRIVERVALE DR       12172.96    4859.65   2.505 0.012325 *  
## StreetRIVERVALE ST       14518.22    7423.24   1.956 0.050626 .  
## StreetRIVERVALE WALK     38977.29    7549.68   5.163 2.67e-07 ***
## StreetSENGKANG CTRL     112045.28    6428.06  17.431  < 2e-16 ***
## StreetSENGKANG EAST AVE 108228.75    5585.73  19.376  < 2e-16 ***
## StreetSENGKANG EAST RD   43523.78   10653.54   4.085 4.57e-05 ***
## StreetSENGKANG EAST WAY  47340.98    5326.87   8.887  < 2e-16 ***
## StreetSENGKANG WEST AVE  12712.42    9163.55   1.387 0.165506    
## StreetSENGKANG WEST WAY -18907.44    4733.58  -3.994 6.72e-05 ***
## Story04 TO 06            25756.39    2346.87  10.975  < 2e-16 ***
## Story07 TO 09            43052.59    2319.59  18.560  < 2e-16 ***
## Story10 TO 12            49553.02    2396.53  20.677  < 2e-16 ***
## Story13 TO 15            57931.02    2320.00  24.970  < 2e-16 ***
## Story16 TO 18            65106.00    2888.96  22.536  < 2e-16 ***
## Story19 TO 21            62530.96    4317.69  14.483  < 2e-16 ***
## Story22 TO 24            70527.74    4870.19  14.482  < 2e-16 ***
## Story25 TO 27            64705.25    6746.42   9.591  < 2e-16 ***
## Area                      2799.77     331.66   8.442  < 2e-16 ***
## ModelModel A             10520.28    3008.99   3.496 0.000482 ***
## ModelModel A2            53641.43    5443.87   9.854  < 2e-16 ***
## ModelPremium Apartment   20304.85    2637.57   7.698 2.12e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29550 on 2061 degrees of freedom
## Multiple R-squared:  0.8854, Adjusted R-squared:  0.8824 
## F-statistic:   295 on 54 and 2061 DF,  p-value: < 2.2e-16

Comparing BIC

BIC_location <- data.frame(lm = c(".-Block",".-Street",".-subzone",".-Block-Street",".-Block-subzone"),
                              BIC = c(BIC(L1),BIC(L2),BIC(L3),BIC(L4),BIC(L5)))
BIC_location
##                lm      BIC
## 1         .-Block 49895.90
## 2        .-Street 52085.02
## 3       .-subzone 52085.02
## 4  .-Block-Street 50966.23
## 5 .-Block-subzone 49941.80

Checking for multicolinearity

We will notice that L4 and L5 have no perfect collinearity in the model. However, under L1, there was only one perfect collinearity found. Using our best model so far, L1, we need to fix the perfect multicolinearity present. We notice from above that L1 in fact, has perfect collinearity between Street and subzone. We will wrangle the data such that we can ommit one street while assign a binary variable to them. We will drop two of the street to ensure we do not have perfect collinerity. It is important to choose streets with a high p-value so as to see the effects of the more significant streets.

df_1 <- df %>%
  tidyr::pivot_wider(names_from = Street,
              values_from = Street, 
              values_fn = list(Street = ~1), 
              values_fill = 0) 
# Run L1 again with new df
L1_modified <- lm(ResalePrice ~.-Block,
                  data = df_1)
summary(L1_modified)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block, data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -125204  -18457    -399   16719  127481 
## 
## Coefficients: (2 not defined because of singularities)
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            211856.8    25911.3   8.176 5.06e-16 ***
## Date2022-02-01           3068.5     3128.1   0.981 0.326734    
## Date2022-03-01           9563.9     3012.9   3.174 0.001524 ** 
## Date2022-04-01          19615.9     2962.6   6.621 4.53e-11 ***
## Date2022-05-01          22646.1     3023.1   7.491 1.01e-13 ***
## Date2022-06-01          30192.6     3101.9   9.734  < 2e-16 ***
## Date2022-07-01          34028.7     2899.6  11.736  < 2e-16 ***
## Date2022-08-01          35919.8     2959.7  12.136  < 2e-16 ***
## Date2022-09-01          46772.6     2968.8  15.755  < 2e-16 ***
## Date2022-10-01          54202.7     3199.5  16.941  < 2e-16 ***
## Date2022-11-01          56565.2     3173.4  17.825  < 2e-16 ***
## Date2022-12-01          63959.6     3084.6  20.735  < 2e-16 ***
## Type4 ROOM              49571.8     8543.0   5.803 7.54e-09 ***
## Type5 ROOM             111733.1    14909.8   7.494 9.87e-14 ***
## years_used              -7932.1      170.6 -46.489  < 2e-16 ***
## subzoneCompassvale      41763.7     9000.7   4.640 3.70e-06 ***
## subzoneFernvale         -8749.9    14952.0  -0.585 0.558481    
## subzoneRivervale       -34279.2     8747.5  -3.919 9.19e-05 ***
## Story04 TO 06           25598.3     2314.9  11.058  < 2e-16 ***
## Story07 TO 09           42935.1     2288.0  18.765  < 2e-16 ***
## Story10 TO 12           48920.3     2365.7  20.679  < 2e-16 ***
## Story13 TO 15           57766.2     2289.7  25.229  < 2e-16 ***
## Story16 TO 18           66007.9     2853.4  23.133  < 2e-16 ***
## Story19 TO 21           62466.9     4258.6  14.668  < 2e-16 ***
## Story22 TO 24           70520.1     4803.4  14.681  < 2e-16 ***
## Story25 TO 27           64791.9     6653.9   9.737  < 2e-16 ***
## Area                     2752.7      327.2   8.413  < 2e-16 ***
## ModelModel A            10459.1     2969.3   3.522 0.000437 ***
## ModelModel A2           52568.6     5375.9   9.778  < 2e-16 ***
## ModelPremium Apartment  20248.1     2601.8   7.782 1.12e-14 ***
## `ANCHORVALE ST`          3690.3    14269.1   0.259 0.795950    
## `COMPASSVALE LANE`     -32307.9    10389.7  -3.110 0.001899 ** 
## `FERNVALE LINK`         -3616.5     7369.5  -0.491 0.623667    
## `FERNVALE RD`            8271.6     7101.2   1.165 0.244229    
## `FERNVALE ST`           -5469.5     8778.4  -0.623 0.533308    
## `RIVERVALE CRES`         8970.1    14117.2   0.635 0.525238    
## `ANCHORVALE CRES`       -1181.8    13779.1  -0.086 0.931662    
## `COMPASSVALE CRES`     -36954.9    10317.3  -3.582 0.000349 ***
## `SENGKANG EAST AVE`     65325.1    11258.2   5.802 7.55e-09 ***
## `SENGKANG WEST AVE`     19881.0    10963.2   1.813 0.069912 .  
## `SENGKANG WEST WAY`    -11630.2     7950.2  -1.463 0.143651    
## `COMPASSVALE DR`        30334.9    10558.3   2.873 0.004106 ** 
## `JLN KAYU`              -5462.2    11594.4  -0.471 0.637613    
## `ANCHORVALE LINK`       11024.2    13676.5   0.806 0.420297    
## `COMPASSVALE BOW`       48523.8    10809.3   4.489 7.55e-06 ***
## `COMPASSVALE ST`       -35391.4    10556.1  -3.353 0.000815 ***
## `COMPASSVALE WALK`       1192.0    11133.6   0.107 0.914749    
## `RIVERVALE ST`          47689.7    15313.6   3.114 0.001870 ** 
## `RIVERVALE WALK`        72099.4    15355.6   4.695 2.84e-06 ***
## `SENGKANG EAST WAY`     44927.8    12102.8   3.712 0.000211 ***
## `ANCHORVALE DR`         30545.9    14202.6   2.151 0.031614 *  
## `RIVERVALE DR`          44987.6    14189.8   3.170 0.001545 ** 
## `ANCHORVALE RD`         -1544.5    13786.7  -0.112 0.910811    
## `COMPASSVALE LINK`      64066.2    10649.2   6.016 2.11e-09 ***
## `FERNVALE LANE`              NA         NA      NA       NA    
## `SENGKANG CTRL`         68978.8    11459.8   6.019 2.07e-09 ***
## `COMPASSVALE RD`         4338.4    10741.2   0.404 0.686327    
## `ANCHORVALE LANE`      -13628.4    14990.0  -0.909 0.363369    
## `SENGKANG EAST RD`           NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29150 on 2058 degrees of freedom
## Multiple R-squared:  0.8887, Adjusted R-squared:  0.8857 
## F-statistic: 293.4 on 56 and 2058 DF,  p-value: < 2.2e-16
# It is understood that Street and Subzone will be correlated. We will remove two variables from Street and rerun
# We will choose ANCHORVALE LANE and FERNVALE RD that have a corresponding p-value of
L6 <- lm(ResalePrice ~.-Block-`ANCHORVALE LANE`-`FERNVALE RD`,
         data = df_1)
summary(L6)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD`, 
##     data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -125204  -18457    -399   16719  127481 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            198228.4    23649.5   8.382  < 2e-16 ***
## Date2022-02-01           3068.5     3128.1   0.981 0.326734    
## Date2022-03-01           9563.9     3012.9   3.174 0.001524 ** 
## Date2022-04-01          19615.9     2962.6   6.621 4.53e-11 ***
## Date2022-05-01          22646.1     3023.1   7.491 1.01e-13 ***
## Date2022-06-01          30192.6     3101.9   9.734  < 2e-16 ***
## Date2022-07-01          34028.7     2899.6  11.736  < 2e-16 ***
## Date2022-08-01          35919.8     2959.7  12.136  < 2e-16 ***
## Date2022-09-01          46772.6     2968.8  15.755  < 2e-16 ***
## Date2022-10-01          54202.7     3199.5  16.941  < 2e-16 ***
## Date2022-11-01          56565.2     3173.4  17.825  < 2e-16 ***
## Date2022-12-01          63959.6     3084.6  20.735  < 2e-16 ***
## Type4 ROOM              49571.8     8543.0   5.803 7.54e-09 ***
## Type5 ROOM             111733.1    14909.8   7.494 9.87e-14 ***
## years_used              -7932.1      170.6 -46.489  < 2e-16 ***
## subzoneCompassvale      41763.7     9000.7   4.640 3.70e-06 ***
## subzoneFernvale         13150.2     7369.0   1.785 0.074486 .  
## subzoneRivervale       -34279.2     8747.5  -3.919 9.19e-05 ***
## Story04 TO 06           25598.3     2314.9  11.058  < 2e-16 ***
## Story07 TO 09           42935.1     2288.0  18.765  < 2e-16 ***
## Story10 TO 12           48920.3     2365.7  20.679  < 2e-16 ***
## Story13 TO 15           57766.2     2289.7  25.229  < 2e-16 ***
## Story16 TO 18           66007.9     2853.4  23.133  < 2e-16 ***
## Story19 TO 21           62466.9     4258.6  14.668  < 2e-16 ***
## Story22 TO 24           70520.1     4803.4  14.681  < 2e-16 ***
## Story25 TO 27           64791.9     6653.9   9.737  < 2e-16 ***
## Area                     2752.7      327.2   8.413  < 2e-16 ***
## ModelModel A            10459.1     2969.3   3.522 0.000437 ***
## ModelModel A2           52568.6     5375.9   9.778  < 2e-16 ***
## ModelPremium Apartment  20248.1     2601.8   7.782 1.12e-14 ***
## `ANCHORVALE ST`         17318.8     8696.0   1.992 0.046550 *  
## `COMPASSVALE LANE`     -18679.5    11877.3  -1.573 0.115942    
## `FERNVALE LINK`        -11888.1     3403.0  -3.493 0.000487 ***
## `FERNVALE ST`          -13741.1     5829.4  -2.357 0.018505 *  
## `RIVERVALE CRES`        22598.5    11459.7   1.972 0.048744 *  
## `ANCHORVALE CRES`       12446.7     7710.3   1.614 0.106617    
## `COMPASSVALE CRES`     -23326.4    11649.6  -2.002 0.045380 *  
## `SENGKANG EAST AVE`     78953.6    12406.7   6.364 2.42e-10 ***
## `SENGKANG WEST AVE`     11609.4     8879.7   1.307 0.191220    
## `SENGKANG WEST WAY`    -19901.8     4576.0  -4.349 1.43e-05 ***
## `COMPASSVALE DR`        43963.3    11841.9   3.713 0.000211 ***
## `JLN KAYU`             -13733.8     9620.7  -1.428 0.153580    
## `ANCHORVALE LINK`       24652.6     7609.3   3.240 0.001215 ** 
## `COMPASSVALE BOW`       62152.2    12198.7   5.095 3.81e-07 ***
## `COMPASSVALE ST`       -21763.0    11874.2  -1.833 0.066978 .  
## `COMPASSVALE WALK`      14820.4    12467.0   1.189 0.234666    
## `RIVERVALE ST`          61318.2    12850.4   4.772 1.96e-06 ***
## `RIVERVALE WALK`        85727.8    12906.3   6.642 3.94e-11 ***
## `SENGKANG EAST WAY`     58556.3     8901.6   6.578 6.02e-11 ***
## `ANCHORVALE DR`         44174.3     8582.0   5.147 2.89e-07 ***
## `RIVERVALE DR`          58616.0    11537.6   5.080 4.11e-07 ***
## `ANCHORVALE RD`         12083.9     7518.9   1.607 0.108178    
## `COMPASSVALE LINK`      77694.6    11889.6   6.535 8.01e-11 ***
## `FERNVALE LANE`         -8271.6     7101.2  -1.165 0.244229    
## `SENGKANG CTRL`         82607.2    12611.3   6.550 7.23e-11 ***
## `COMPASSVALE RD`        17966.8    12186.3   1.474 0.140543    
## `SENGKANG EAST RD`      13628.4    14990.0   0.909 0.363369    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29150 on 2058 degrees of freedom
## Multiple R-squared:  0.8887, Adjusted R-squared:  0.8857 
## F-statistic: 293.4 on 56 and 2058 DF,  p-value: < 2.2e-16
BIC(L6)
## [1] 49873.17

We notice that after removing the 2 variables BIC lowers to 49873.17, lower than initially calculated. We also see that adjusted R square maintains at 0.8857.

library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
v <- vif(L6)
v
##                             GVIF Df GVIF^(1/(2*Df))
## Date                    1.302178 11        1.012074
## Type                   76.773410  2        2.960075
## years_used              3.605298  1        1.898762
## subzone             14287.238357  3        4.925966
## Story                   1.603685  8        1.029959
## Area                   48.537346  1        6.966875
## Model                   9.598688  3        1.457814
## `ANCHORVALE ST`         3.321897  1        1.822607
## `COMPASSVALE LANE`     15.067342  1        3.881667
## `FERNVALE LINK`         2.730191  1        1.652329
## `FERNVALE ST`           1.299454  1        1.139936
## `RIVERVALE CRES`       25.842308  1        5.083533
## `ANCHORVALE CRES`       8.107005  1        2.847280
## `COMPASSVALE CRES`     35.704792  1        5.975349
## `SENGKANG EAST AVE`     6.936304  1        2.633686
## `SENGKANG WEST AVE`     1.107502  1        1.052379
## `SENGKANG WEST WAY`     1.552948  1        1.246173
## `COMPASSVALE DR`       13.619144  1        3.690412
## `JLN KAYU`              1.084400  1        1.041345
## `ANCHORVALE LINK`       5.873349  1        2.423499
## `COMPASSVALE BOW`       8.718329  1        2.952682
## `COMPASSVALE ST`        9.676052  1        3.110635
## `COMPASSVALE WALK`      9.974519  1        3.158246
## `RIVERVALE ST`          5.559951  1        2.357955
## `RIVERVALE WALK`        5.798992  1        2.408110
## `SENGKANG EAST WAY`     5.788975  1        2.406029
## `ANCHORVALE DR`         2.984216  1        1.727488
## `RIVERVALE DR`         17.179966  1        4.144872
## `ANCHORVALE RD`         5.061038  1        2.249675
## `COMPASSVALE LINK`     10.639994  1        3.261900
## `FERNVALE LANE`         1.175986  1        1.084429
## `SENGKANG CTRL`         5.354950  1        2.314076
## `COMPASSVALE RD`        7.866644  1        2.804754
## `SENGKANG EAST RD`      2.370449  1        1.539626

Generally, GVIF above 2 or 3 to suggest potential multi-collinearity. Given that Street and subzone is correlated in some ways due to roads intersections with the subzones, we will bound to see some collinearity there. However, both categories are still useful for its own interpretation. For example, subzone indicates neighbourhoods clustering. There could be other variables such as proximity of schools, clinics and other facilities that attribute to the popularity of the subzone. As for streets, it could be that some streets have more buses operating or that some streets leads to expressway, contributing to ease of commute. hence, even though there are some VIF scores of 5, they are still within acceptable basis.

Visualize L6

plot(L6)

Note: We will be using L1 as the main regression and adding on to that regression. We know that the model is linear as checked under residual plots assumptions.

tmap_mode("view")
## tmap mode set to interactive viewing
tm_shape(sengkang_sp) +
  tm_dots(col = "Area")

For visualisation purposes, we plotted the Area. We notice that there is clustering of large area flats within one particular sub district. We can create an interactive term between Area and subzone.

L7 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone,
         data = df_1)
summary(L7)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone, data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -125977  -18061    -289   16396  124563 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             204273.9    27855.9   7.333 3.22e-13 ***
## Date2022-02-01            3042.7     3096.6   0.983 0.325923    
## Date2022-03-01            9210.3     2983.3   3.087 0.002047 ** 
## Date2022-04-01           19000.8     2934.7   6.475 1.19e-10 ***
## Date2022-05-01           21937.2     2994.5   7.326 3.39e-13 ***
## Date2022-06-01           29310.4     3077.3   9.525  < 2e-16 ***
## Date2022-07-01           33893.8     2874.7  11.791  < 2e-16 ***
## Date2022-08-01           36487.0     2931.3  12.447  < 2e-16 ***
## Date2022-09-01           46667.2     2939.9  15.874  < 2e-16 ***
## Date2022-10-01           53800.5     3168.1  16.982  < 2e-16 ***
## Date2022-11-01           56026.9     3142.9  17.827  < 2e-16 ***
## Date2022-12-01           63992.3     3055.8  20.941  < 2e-16 ***
## Type4 ROOM               55239.6     8690.0   6.357 2.53e-10 ***
## Type5 ROOM              117645.9    15009.3   7.838 7.28e-15 ***
## years_used               -7923.4      169.7 -46.689  < 2e-16 ***
## subzoneCompassvale       14277.6    18266.1   0.782 0.434512    
## subzoneFernvale          33991.8    17842.1   1.905 0.056901 .  
## subzoneRivervale         52884.5    20815.0   2.541 0.011137 *  
## Story04 TO 06            25872.9     2293.0  11.283  < 2e-16 ***
## Story07 TO 09            42763.9     2265.2  18.879  < 2e-16 ***
## Story10 TO 12            49393.1     2342.8  21.083  < 2e-16 ***
## Story13 TO 15            57932.5     2268.2  25.542  < 2e-16 ***
## Story16 TO 18            66590.9     2826.4  23.561  < 2e-16 ***
## Story19 TO 21            62389.3     4235.1  14.731  < 2e-16 ***
## Story22 TO 24            70534.8     4754.9  14.834  < 2e-16 ***
## Story25 TO 27            65111.8     6587.9   9.883  < 2e-16 ***
## Area                      2652.7      361.9   7.330 3.30e-13 ***
## ModelModel A              4902.8     3069.7   1.597 0.110378    
## ModelModel A2            43160.5     5518.0   7.822 8.26e-15 ***
## ModelPremium Apartment   18540.2     2588.4   7.163 1.10e-12 ***
## `ANCHORVALE ST`          19157.0     8634.8   2.219 0.026624 *  
## `COMPASSVALE LANE`      -12564.0    11810.8  -1.064 0.287556    
## `FERNVALE LINK`         -11095.2     3372.6  -3.290 0.001019 ** 
## `FERNVALE ST`           -12749.5     5791.3  -2.202 0.027811 *  
## `RIVERVALE CRES`         17316.0    11386.2   1.521 0.128467    
## `ANCHORVALE CRES`        13826.8     7667.6   1.803 0.071493 .  
## `COMPASSVALE CRES`      -20526.0    11539.8  -1.779 0.075434 .  
## `SENGKANG EAST AVE`      82276.7    12292.2   6.693 2.80e-11 ***
## `SENGKANG WEST AVE`      12352.7     8799.4   1.404 0.160525    
## `SENGKANG WEST WAY`     -19241.7     4534.1  -4.244 2.30e-05 ***
## `COMPASSVALE DR`         46908.9    11732.1   3.998 6.60e-05 ***
## `JLN KAYU`              -12592.7     9526.5  -1.322 0.186365    
## `ANCHORVALE LINK`        26486.7     7546.1   3.510 0.000458 ***
## `COMPASSVALE BOW`        65764.5    12089.2   5.440 5.97e-08 ***
## `COMPASSVALE ST`        -20992.5    11754.9  -1.786 0.074271 .  
## `COMPASSVALE WALK`       15736.7    12344.3   1.275 0.202517    
## `RIVERVALE ST`           67939.5    12764.4   5.323 1.13e-07 ***
## `RIVERVALE WALK`         93255.6    12831.9   7.267 5.18e-13 ***
## `SENGKANG EAST WAY`      59481.7     8814.6   6.748 1.94e-11 ***
## `ANCHORVALE DR`          44328.0     8498.1   5.216 2.01e-07 ***
## `RIVERVALE DR`           60519.7    11426.4   5.296 1.31e-07 ***
## `ANCHORVALE RD`          12009.2     7443.1   1.613 0.106795    
## `COMPASSVALE LINK`       80880.9    11783.9   6.864 8.85e-12 ***
## `FERNVALE LANE`          -9426.8     7033.2  -1.340 0.180287    
## `SENGKANG CTRL`          86053.1    12501.3   6.884 7.73e-12 ***
## `COMPASSVALE RD`         18718.9    12064.1   1.552 0.120908    
## `SENGKANG EAST RD`       17259.4    14851.6   1.162 0.245320    
## subzoneCompassvale:Area    252.7      155.1   1.630 0.103319    
## subzoneFernvale:Area      -203.1      163.8  -1.240 0.215144    
## subzoneRivervale:Area     -832.4      182.8  -4.555 5.55e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 28850 on 2055 degrees of freedom
## Multiple R-squared:  0.8911, Adjusted R-squared:  0.888 
## F-statistic:   285 on 59 and 2055 DF,  p-value: < 2.2e-16
BIC(L7)
## [1] 49850.05

We notice that adjusted R square went up and BIC went down to 49850 as compared to 49873.17. We notice that subzone are no longer significant except for rivervale. We can say that the interaction between Area and subzone is condensed in Rivervale and that contributes to the Resale price. We know that area is also affected by the number of rooms under type. We will add Type into the interaction as well.

L8 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type,
         data = df_1)
summary(L8)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type, data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -121050  -16012    -783   15722  124041 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          201726.3    67872.8   2.972 0.002992 ** 
## Date2022-02-01                         2933.9     3024.5   0.970 0.332137    
## Date2022-03-01                         9030.3     2921.3   3.091 0.002021 ** 
## Date2022-04-01                        18580.7     2872.6   6.468 1.24e-10 ***
## Date2022-05-01                        21617.5     2929.5   7.379 2.30e-13 ***
## Date2022-06-01                        27876.9     3012.9   9.253  < 2e-16 ***
## Date2022-07-01                        33426.3     2806.8  11.909  < 2e-16 ***
## Date2022-08-01                        36511.7     2862.2  12.757  < 2e-16 ***
## Date2022-09-01                        45744.8     2867.3  15.954  < 2e-16 ***
## Date2022-10-01                        52972.0     3091.6  17.134  < 2e-16 ***
## Date2022-11-01                        55415.7     3065.8  18.076  < 2e-16 ***
## Date2022-12-01                        63696.4     2987.8  21.319  < 2e-16 ***
## Type4 ROOM                           274443.1   144208.6   1.903 0.057168 .  
## Type5 ROOM                         -1439284.4   240576.7  -5.983 2.59e-09 ***
## years_used                            -7733.8      172.0 -44.951  < 2e-16 ***
## subzoneCompassvale                  -690537.7   694378.7  -0.994 0.320113    
## subzoneFernvale                     -359649.6   303141.4  -1.186 0.235599    
## subzoneRivervale                     404541.5  1011075.6   0.400 0.689117    
## Story04 TO 06                         25629.5     2236.8  11.458  < 2e-16 ***
## Story07 TO 09                         42330.2     2210.3  19.151  < 2e-16 ***
## Story10 TO 12                         49159.9     2287.4  21.492  < 2e-16 ***
## Story13 TO 15                         58066.9     2215.7  26.207  < 2e-16 ***
## Story16 TO 18                         66267.0     2758.7  24.021  < 2e-16 ***
## Story19 TO 21                         64825.2     4157.2  15.594  < 2e-16 ***
## Story22 TO 24                         71094.7     4647.9  15.296  < 2e-16 ***
## Story25 TO 27                         64999.1     6431.0  10.107  < 2e-16 ***
## Area                                   2757.1      948.4   2.907 0.003688 ** 
## ModelModel A                           5869.4     3069.1   1.912 0.055961 .  
## ModelModel A2                         32272.9     6141.3   5.255 1.63e-07 ***
## ModelPremium Apartment                20664.1     2574.6   8.026 1.68e-15 ***
## `ANCHORVALE ST`                       20932.8     8492.9   2.465 0.013793 *  
## `COMPASSVALE LANE`                     7247.8    12039.3   0.602 0.547233    
## `FERNVALE LINK`                       -5687.1     3452.1  -1.647 0.099620 .  
## `FERNVALE ST`                         -7426.9     5787.4  -1.283 0.199536    
## `RIVERVALE CRES`                      25980.5    11430.6   2.273 0.023136 *  
## `ANCHORVALE CRES`                     14455.8     7596.8   1.903 0.057195 .  
## `COMPASSVALE CRES`                    -4195.3    11633.0  -0.361 0.718410    
## `SENGKANG EAST AVE`                   98262.7    12341.7   7.962 2.79e-15 ***
## `SENGKANG WEST AVE`                   11918.1     8701.6   1.370 0.170951    
## `SENGKANG WEST WAY`                  -10134.6     4838.3  -2.095 0.036322 *  
## `COMPASSVALE DR`                      62430.7    11760.1   5.309 1.22e-07 ***
## `JLN KAYU`                            -6323.7     9337.3  -0.677 0.498327    
## `ANCHORVALE LINK`                     34667.2     7537.2   4.599 4.50e-06 ***
## `COMPASSVALE BOW`                     79783.8    12174.1   6.554 7.09e-11 ***
## `COMPASSVALE ST`                      -7342.6    11702.9  -0.627 0.530458    
## `COMPASSVALE WALK`                    47510.1    13037.0   3.644 0.000275 ***
## `RIVERVALE ST`                        72494.2    13445.7   5.392 7.79e-08 ***
## `RIVERVALE WALK`                      96714.2    13661.8   7.079 1.99e-12 ***
## `SENGKANG EAST WAY`                   69556.3     8810.0   7.895 4.69e-15 ***
## `ANCHORVALE DR`                       59855.9     8703.7   6.877 8.09e-12 ***
## `RIVERVALE DR`                        67900.3    11462.6   5.924 3.69e-09 ***
## `ANCHORVALE RD`                       20303.6     7335.3   2.768 0.005693 ** 
## `COMPASSVALE LINK`                    87894.1    11806.8   7.444 1.43e-13 ***
## `FERNVALE LANE`                       -5720.4     6951.1  -0.823 0.410631    
## `SENGKANG CTRL`                       97427.9    12523.2   7.780 1.14e-14 ***
## `COMPASSVALE RD`                      30827.3    11935.9   2.583 0.009871 ** 
## `SENGKANG EAST RD`                    24835.6    14641.8   1.696 0.089999 .  
## subzoneCompassvale:Area               10191.1    10243.6   0.995 0.319912    
## subzoneFernvale:Area                   5475.7     4453.1   1.230 0.218971    
## subzoneRivervale:Area                 -6444.4    15020.1  -0.429 0.667929    
## Type4 ROOM:Area                       -2563.1     1697.3  -1.510 0.131186    
## Type5 ROOM:Area                       13854.6     2315.6   5.983 2.58e-09 ***
## Type4 ROOM:subzoneCompassvale        740624.5   707494.0   1.047 0.295303    
## Type5 ROOM:subzoneCompassvale       2425708.5   735130.9   3.300 0.000985 ***
## Type4 ROOM:subzoneFernvale          -438453.5   347325.1  -1.262 0.206959    
## Type5 ROOM:subzoneFernvale          1630054.0   455450.3   3.579 0.000353 ***
## Type4 ROOM:subzoneRivervale         -564324.5  1019144.7  -0.554 0.579829    
## Type5 ROOM:subzoneRivervale         1124902.3  1040440.2   1.081 0.279745    
## Type4 ROOM:subzoneCompassvale:Area   -10393.9    10353.0  -1.004 0.315522    
## Type5 ROOM:subzoneCompassvale:Area   -25493.0    10481.7  -2.432 0.015095 *  
## Type4 ROOM:subzoneFernvale:Area        3277.5     4792.9   0.684 0.494170    
## Type5 ROOM:subzoneFernvale:Area      -16815.2     5380.6  -3.125 0.001802 ** 
## Type4 ROOM:subzoneRivervale:Area       7959.0    15088.2   0.528 0.597902    
## Type5 ROOM:subzoneRivervale:Area      -7730.8    15191.2  -0.509 0.610878    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 28090 on 2041 degrees of freedom
## Multiple R-squared:  0.8975, Adjusted R-squared:  0.8938 
## F-statistic: 244.7 on 73 and 2041 DF,  p-value: < 2.2e-16
BIC(L8)
## [1] 49829.95

We will want to include another interaction variable here. This time with Model. Model indicates the current condition of the house as well. Base on the research done, Model A and A2 are older generation models, Premium has a similar structure to Model A and A2 but comes with newer amenities, Improved are units that went through upgrading works. We will interact Model with the years_used.

L9 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used,
         data = df_1)
summary(L9)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type + Model * years_used, data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -118353  -16184   -1043   15695  119172 
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         245281.7    65576.9   3.740 0.000189 ***
## Date2022-02-01                        2394.9     2917.3   0.821 0.411776    
## Date2022-03-01                        9391.9     2821.7   3.328 0.000889 ***
## Date2022-04-01                       18053.0     2772.9   6.511 9.40e-11 ***
## Date2022-05-01                       23021.6     2831.0   8.132 7.25e-16 ***
## Date2022-06-01                       28804.4     2906.2   9.911  < 2e-16 ***
## Date2022-07-01                       33304.4     2707.6  12.300  < 2e-16 ***
## Date2022-08-01                       36381.7     2762.2  13.171  < 2e-16 ***
## Date2022-09-01                       46212.6     2769.1  16.689  < 2e-16 ***
## Date2022-10-01                       53990.9     2982.5  18.102  < 2e-16 ***
## Date2022-11-01                       56670.3     2957.4  19.162  < 2e-16 ***
## Date2022-12-01                       62995.0     2881.1  21.865  < 2e-16 ***
## Type4 ROOM                           83233.3   141821.6   0.587 0.557344    
## Type5 ROOM                         -671659.3   241994.2  -2.776 0.005562 ** 
## years_used                           -9209.5      259.3 -35.511  < 2e-16 ***
## subzoneCompassvale                 -771233.7   669598.3  -1.152 0.249544    
## subzoneFernvale                    -267509.2   292326.6  -0.915 0.360245    
## subzoneRivervale                    134314.6   974950.1   0.138 0.890439    
## Story04 TO 06                        25257.5     2157.1  11.709  < 2e-16 ***
## Story07 TO 09                        42614.0     2135.3  19.957  < 2e-16 ***
## Story10 TO 12                        49925.6     2206.4  22.627  < 2e-16 ***
## Story13 TO 15                        58014.0     2136.3  27.156  < 2e-16 ***
## Story16 TO 18                        65888.8     2660.9  24.762  < 2e-16 ***
## Story19 TO 21                        65345.5     4008.2  16.303  < 2e-16 ***
## Story22 TO 24                        70850.3     4481.1  15.811  < 2e-16 ***
## Story25 TO 27                        65073.7     6199.8  10.496  < 2e-16 ***
## Area                                  2510.5      914.7   2.745 0.006109 ** 
## ModelModel A                        -40099.9     5049.9  -7.941 3.29e-15 ***
## ModelModel A2                       -72339.8    60839.8  -1.189 0.234570    
## ModelPremium Apartment                9967.3     5364.0   1.858 0.063284 .  
## `ANCHORVALE ST`                      14575.8     8256.4   1.765 0.077647 .  
## `COMPASSVALE LANE`                   -3329.8    11702.6  -0.285 0.776026    
## `FERNVALE LINK`                      -1946.7     3350.2  -0.581 0.561269    
## `FERNVALE ST`                        -6213.7     5586.3  -1.112 0.266138    
## `RIVERVALE CRES`                     13593.4    11082.0   1.227 0.220109    
## `ANCHORVALE CRES`                     7399.0     7473.0   0.990 0.322244    
## `COMPASSVALE CRES`                  -24176.1    11466.4  -2.108 0.035116 *  
## `SENGKANG EAST AVE`                  78623.1    12135.6   6.479 1.16e-10 ***
## `SENGKANG WEST AVE`                   8217.2     8395.6   0.979 0.327821    
## `SENGKANG WEST WAY`                 -10711.8     4665.8  -2.296 0.021788 *  
## `COMPASSVALE DR`                     43365.4    11616.0   3.733 0.000194 ***
## `JLN KAYU`                           -8205.6     9002.7  -0.911 0.362165    
## `ANCHORVALE LINK`                    26020.1     7384.0   3.524 0.000435 ***
## `COMPASSVALE BOW`                    68171.4    11783.7   5.785 8.36e-09 ***
## `COMPASSVALE ST`                    -17662.3    11330.4  -1.559 0.119189    
## `COMPASSVALE WALK`                   28033.3    12850.7   2.181 0.029264 *  
## `RIVERVALE ST`                       47835.6    13277.2   3.603 0.000322 ***
## `RIVERVALE WALK`                     71016.9    13528.3   5.250 1.68e-07 ***
## `SENGKANG EAST WAY`                  57057.0     8760.3   6.513 9.25e-11 ***
## `ANCHORVALE DR`                      49833.7     8661.0   5.754 1.00e-08 ***
## `RIVERVALE DR`                       49599.5    11283.4   4.396 1.16e-05 ***
## `ANCHORVALE RD`                      11597.1     7208.4   1.609 0.107809    
## `COMPASSVALE LINK`                   76107.8    11437.2   6.654 3.64e-11 ***
## `FERNVALE LANE`                      -2076.6     6754.5  -0.307 0.758542    
## `SENGKANG CTRL`                      85004.7    12144.7   6.999 3.48e-12 ***
## `COMPASSVALE RD`                     20138.1    11703.0   1.721 0.085446 .  
## `SENGKANG EAST RD`                    2441.2    14343.7   0.170 0.864874    
## subzoneCompassvale:Area              11514.2     9878.1   1.166 0.243900    
## subzoneFernvale:Area                  4146.3     4294.2   0.966 0.334373    
## subzoneRivervale:Area                -2169.4    14483.9  -0.150 0.880951    
## Type4 ROOM:Area                       -347.3     1666.3  -0.208 0.834923    
## Type5 ROOM:Area                       7075.1     2315.6   3.055 0.002276 ** 
## Type4 ROOM:subzoneCompassvale      1067016.7   682906.2   1.562 0.118334    
## Type5 ROOM:subzoneCompassvale      1665016.7   711517.8   2.340 0.019375 *  
## Type4 ROOM:subzoneFernvale         -213984.0   336280.7  -0.636 0.524636    
## Type5 ROOM:subzoneFernvale          650272.8   447108.7   1.454 0.145991    
## Type4 ROOM:subzoneRivervale         -68586.7   983529.5  -0.070 0.944411    
## Type5 ROOM:subzoneRivervale         495092.3  1004994.9   0.493 0.622326    
## years_used:ModelModel A               3484.0      292.7  11.903  < 2e-16 ***
## years_used:ModelModel A2              5419.1     2789.7   1.943 0.052207 .  
## years_used:ModelPremium Apartment      516.3      342.5   1.508 0.131819    
## Type4 ROOM:subzoneCompassvale:Area  -14371.0     9989.2  -1.439 0.150402    
## Type5 ROOM:subzoneCompassvale:Area  -19168.9    10117.6  -1.895 0.058284 .  
## Type4 ROOM:subzoneFernvale:Area       1125.6     4632.2   0.243 0.808031    
## Type5 ROOM:subzoneFernvale:Area      -7666.3     5245.7  -1.461 0.144050    
## Type4 ROOM:subzoneRivervale:Area      1224.5    14557.6   0.084 0.932976    
## Type5 ROOM:subzoneRivervale:Area     -3786.0    14653.0  -0.258 0.796142    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27080 on 2038 degrees of freedom
## Multiple R-squared:  0.9048, Adjusted R-squared:  0.9013 
## F-statistic:   255 on 76 and 2038 DF,  p-value: < 2.2e-16
BIC(L9)
## [1] 49694.8

Generally, I would like to know whether higher floors tend to have higher prices.

L10 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2),
         data = df_1)
summary(L10)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type + Model * years_used + I(Area^2), data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -118136  -16436   -1070   15593  118433 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                        1639149.46  405856.27   4.039 5.57e-05 ***
## Date2022-02-01                        2552.64    2909.75   0.877 0.380443    
## Date2022-03-01                        9703.18    2815.49   3.446 0.000580 ***
## Date2022-04-01                       17941.67    2765.56   6.488 1.09e-10 ***
## Date2022-05-01                       23277.17    2824.25   8.242 3.00e-16 ***
## Date2022-06-01                       28871.82    2898.42   9.961  < 2e-16 ***
## Date2022-07-01                       33243.16    2700.32  12.311  < 2e-16 ***
## Date2022-08-01                       36514.12    2754.98  13.254  < 2e-16 ***
## Date2022-09-01                       46260.79    2761.64  16.751  < 2e-16 ***
## Date2022-10-01                       54137.47    2974.72  18.199  < 2e-16 ***
## Date2022-11-01                       57043.75    2951.36  19.328  < 2e-16 ***
## Date2022-12-01                       63219.73    2874.00  21.997  < 2e-16 ***
## Type4 ROOM                          854842.23  263003.64   3.250 0.001172 ** 
## Type5 ROOM                         1091014.45  561089.81   1.944 0.051978 .  
## years_used                           -9545.26     276.05 -34.578  < 2e-16 ***
## subzoneCompassvale                 -981975.20  670521.14  -1.464 0.143213    
## subzoneFernvale                    -525977.23  300846.07  -1.748 0.080558 .  
## subzoneRivervale                    -88803.07  974415.38  -0.091 0.927395    
## Story04 TO 06                        25505.50    2152.47  11.849  < 2e-16 ***
## Story07 TO 09                        42737.63    2129.75  20.067  < 2e-16 ***
## Story10 TO 12                        50085.71    2200.93  22.757  < 2e-16 ***
## Story13 TO 15                        58418.23    2133.66  27.379  < 2e-16 ***
## Story16 TO 18                        66376.12    2657.35  24.978  < 2e-16 ***
## Story19 TO 21                        65420.22    3997.41  16.366  < 2e-16 ***
## Story22 TO 24                        71070.57    4469.41  15.902  < 2e-16 ***
## Story25 TO 27                        65491.44    6184.09  10.590  < 2e-16 ***
## Area                                -34697.85   10731.32  -3.233 0.001243 ** 
## ModelModel A                        -39812.45    5036.84  -7.904 4.38e-15 ***
## ModelModel A2                      -149274.99   64577.18  -2.312 0.020900 *  
## ModelPremium Apartment                8576.08    5364.32   1.599 0.110036    
## `ANCHORVALE ST`                      13651.48    8238.26   1.657 0.097657 .  
## `COMPASSVALE LANE`                   -2111.25   11676.06  -0.181 0.856528    
## `FERNVALE LINK`                      -2823.59    3350.64  -0.843 0.399495    
## `FERNVALE ST`                        -6932.60    5574.98  -1.244 0.213819    
## `RIVERVALE CRES`                     14743.64   11056.87   1.333 0.182538    
## `ANCHORVALE CRES`                     5944.91    7464.43   0.796 0.425874    
## `COMPASSVALE CRES`                  -22872.78   11441.39  -1.999 0.045727 *  
## `SENGKANG EAST AVE`                  79115.85   12103.48   6.537 7.93e-11 ***
## `SENGKANG WEST AVE`                   9170.49    8377.28   1.095 0.273783    
## `SENGKANG WEST WAY`                 -11190.02    4655.19  -2.404 0.016316 *  
## `COMPASSVALE DR`                     43803.20   11585.15   3.781 0.000161 ***
## `JLN KAYU`                           -7837.35    8978.92  -0.873 0.382842    
## `ANCHORVALE LINK`                    25773.28    7364.31   3.500 0.000476 ***
## `COMPASSVALE BOW`                    68926.23   11753.68   5.864 5.25e-09 ***
## `COMPASSVALE ST`                    -15064.32   11324.25  -1.330 0.183578    
## `COMPASSVALE WALK`                   27134.07   12818.45   2.117 0.034398 *  
## `RIVERVALE ST`                       49632.43   13251.20   3.746 0.000185 ***
## `RIVERVALE WALK`                     69563.02   13498.03   5.154 2.80e-07 ***
## `SENGKANG EAST WAY`                  58682.80    8749.03   6.707 2.56e-11 ***
## `ANCHORVALE DR`                      51167.60    8645.98   5.918 3.81e-09 ***
## `RIVERVALE DR`                       54279.10   11332.82   4.790 1.79e-06 ***
## `ANCHORVALE RD`                      11385.84    7189.11   1.584 0.113403    
## `COMPASSVALE LINK`                   74844.31   11411.95   6.558 6.87e-11 ***
## `FERNVALE LANE`                       -683.04    6748.01  -0.101 0.919385    
## `SENGKANG CTRL`                      85719.19   12113.48   7.076 2.03e-12 ***
## `COMPASSVALE RD`                     22916.26   11698.50   1.959 0.050260 .  
## `SENGKANG EAST RD`                    3960.27   14311.39   0.277 0.782022    
## I(Area^2)                              245.71      70.61   3.480 0.000512 ***
## subzoneCompassvale:Area              14631.15    9891.87   1.479 0.139266    
## subzoneFernvale:Area                  7987.42    4422.49   1.806 0.071052 .  
## subzoneRivervale:Area                 1117.05   14475.40   0.077 0.938497    
## Type4 ROOM:Area                      -9245.26    3049.53  -3.032 0.002462 ** 
## Type5 ROOM:Area                     -11390.93    5787.25  -1.968 0.049171 *  
## Type4 ROOM:subzoneCompassvale      1309674.79  684613.02   1.913 0.055886 .  
## Type5 ROOM:subzoneCompassvale      1996740.57  715960.91   2.789 0.005338 ** 
## Type4 ROOM:subzoneFernvale           17284.62  341889.50   0.051 0.959684    
## Type5 ROOM:subzoneFernvale          859177.64  449918.05   1.910 0.056321 .  
## Type4 ROOM:subzoneRivervale         204833.76  984001.77   0.208 0.835122    
## Type5 ROOM:subzoneRivervale         810247.73 1006350.30   0.805 0.420836    
## years_used:ModelModel A               3443.57     292.15  11.787  < 2e-16 ***
## years_used:ModelModel A2              8458.97    2916.02   2.901 0.003761 ** 
## years_used:ModelPremium Apartment      691.36     345.25   2.002 0.045365 *  
## Type4 ROOM:subzoneCompassvale:Area  -17851.93   10012.15  -1.783 0.074731 .  
## Type5 ROOM:subzoneCompassvale:Area  -23378.48   10162.35  -2.300 0.021521 *  
## Type4 ROOM:subzoneFernvale:Area      -2425.48    4730.96  -0.513 0.608228    
## Type5 ROOM:subzoneFernvale:Area     -11069.70    5322.12  -2.080 0.037656 *  
## Type4 ROOM:subzoneRivervale:Area     -2630.18   14560.30  -0.181 0.856667    
## Type5 ROOM:subzoneRivervale:Area     -7915.74   14661.36  -0.540 0.589322    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27010 on 2037 degrees of freedom
## Multiple R-squared:  0.9054, Adjusted R-squared:  0.9018 
## F-statistic: 253.2 on 77 and 2037 DF,  p-value: < 2.2e-16
BIC(L10)
## [1] 49689.92

I am alittle skeptical whether the relationship between Area and Resale Price, years_used and Resale price is linear due to the plots above.

We will test the regression between Resale Price and this variable alone to see whether higher terms would result in a better result

BIC for L10 decreased while Adjusted Rsquare went up, suggesting that this is a better model.

L11 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2),
         data = df_1)
summary(L11)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type + Model * years_used + I(Area^2), data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -118136  -16436   -1070   15593  118433 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                        1639149.46  405856.27   4.039 5.57e-05 ***
## Date2022-02-01                        2552.64    2909.75   0.877 0.380443    
## Date2022-03-01                        9703.18    2815.49   3.446 0.000580 ***
## Date2022-04-01                       17941.67    2765.56   6.488 1.09e-10 ***
## Date2022-05-01                       23277.17    2824.25   8.242 3.00e-16 ***
## Date2022-06-01                       28871.82    2898.42   9.961  < 2e-16 ***
## Date2022-07-01                       33243.16    2700.32  12.311  < 2e-16 ***
## Date2022-08-01                       36514.12    2754.98  13.254  < 2e-16 ***
## Date2022-09-01                       46260.79    2761.64  16.751  < 2e-16 ***
## Date2022-10-01                       54137.47    2974.72  18.199  < 2e-16 ***
## Date2022-11-01                       57043.75    2951.36  19.328  < 2e-16 ***
## Date2022-12-01                       63219.73    2874.00  21.997  < 2e-16 ***
## Type4 ROOM                          854842.23  263003.64   3.250 0.001172 ** 
## Type5 ROOM                         1091014.45  561089.81   1.944 0.051978 .  
## years_used                           -9545.26     276.05 -34.578  < 2e-16 ***
## subzoneCompassvale                 -981975.20  670521.14  -1.464 0.143213    
## subzoneFernvale                    -525977.23  300846.07  -1.748 0.080558 .  
## subzoneRivervale                    -88803.07  974415.38  -0.091 0.927395    
## Story04 TO 06                        25505.50    2152.47  11.849  < 2e-16 ***
## Story07 TO 09                        42737.63    2129.75  20.067  < 2e-16 ***
## Story10 TO 12                        50085.71    2200.93  22.757  < 2e-16 ***
## Story13 TO 15                        58418.23    2133.66  27.379  < 2e-16 ***
## Story16 TO 18                        66376.12    2657.35  24.978  < 2e-16 ***
## Story19 TO 21                        65420.22    3997.41  16.366  < 2e-16 ***
## Story22 TO 24                        71070.57    4469.41  15.902  < 2e-16 ***
## Story25 TO 27                        65491.44    6184.09  10.590  < 2e-16 ***
## Area                                -34697.85   10731.32  -3.233 0.001243 ** 
## ModelModel A                        -39812.45    5036.84  -7.904 4.38e-15 ***
## ModelModel A2                      -149274.99   64577.18  -2.312 0.020900 *  
## ModelPremium Apartment                8576.08    5364.32   1.599 0.110036    
## `ANCHORVALE ST`                      13651.48    8238.26   1.657 0.097657 .  
## `COMPASSVALE LANE`                   -2111.25   11676.06  -0.181 0.856528    
## `FERNVALE LINK`                      -2823.59    3350.64  -0.843 0.399495    
## `FERNVALE ST`                        -6932.60    5574.98  -1.244 0.213819    
## `RIVERVALE CRES`                     14743.64   11056.87   1.333 0.182538    
## `ANCHORVALE CRES`                     5944.91    7464.43   0.796 0.425874    
## `COMPASSVALE CRES`                  -22872.78   11441.39  -1.999 0.045727 *  
## `SENGKANG EAST AVE`                  79115.85   12103.48   6.537 7.93e-11 ***
## `SENGKANG WEST AVE`                   9170.49    8377.28   1.095 0.273783    
## `SENGKANG WEST WAY`                 -11190.02    4655.19  -2.404 0.016316 *  
## `COMPASSVALE DR`                     43803.20   11585.15   3.781 0.000161 ***
## `JLN KAYU`                           -7837.35    8978.92  -0.873 0.382842    
## `ANCHORVALE LINK`                    25773.28    7364.31   3.500 0.000476 ***
## `COMPASSVALE BOW`                    68926.23   11753.68   5.864 5.25e-09 ***
## `COMPASSVALE ST`                    -15064.32   11324.25  -1.330 0.183578    
## `COMPASSVALE WALK`                   27134.07   12818.45   2.117 0.034398 *  
## `RIVERVALE ST`                       49632.43   13251.20   3.746 0.000185 ***
## `RIVERVALE WALK`                     69563.02   13498.03   5.154 2.80e-07 ***
## `SENGKANG EAST WAY`                  58682.80    8749.03   6.707 2.56e-11 ***
## `ANCHORVALE DR`                      51167.60    8645.98   5.918 3.81e-09 ***
## `RIVERVALE DR`                       54279.10   11332.82   4.790 1.79e-06 ***
## `ANCHORVALE RD`                      11385.84    7189.11   1.584 0.113403    
## `COMPASSVALE LINK`                   74844.31   11411.95   6.558 6.87e-11 ***
## `FERNVALE LANE`                       -683.04    6748.01  -0.101 0.919385    
## `SENGKANG CTRL`                      85719.19   12113.48   7.076 2.03e-12 ***
## `COMPASSVALE RD`                     22916.26   11698.50   1.959 0.050260 .  
## `SENGKANG EAST RD`                    3960.27   14311.39   0.277 0.782022    
## I(Area^2)                              245.71      70.61   3.480 0.000512 ***
## subzoneCompassvale:Area              14631.15    9891.87   1.479 0.139266    
## subzoneFernvale:Area                  7987.42    4422.49   1.806 0.071052 .  
## subzoneRivervale:Area                 1117.05   14475.40   0.077 0.938497    
## Type4 ROOM:Area                      -9245.26    3049.53  -3.032 0.002462 ** 
## Type5 ROOM:Area                     -11390.93    5787.25  -1.968 0.049171 *  
## Type4 ROOM:subzoneCompassvale      1309674.79  684613.02   1.913 0.055886 .  
## Type5 ROOM:subzoneCompassvale      1996740.57  715960.91   2.789 0.005338 ** 
## Type4 ROOM:subzoneFernvale           17284.62  341889.50   0.051 0.959684    
## Type5 ROOM:subzoneFernvale          859177.64  449918.05   1.910 0.056321 .  
## Type4 ROOM:subzoneRivervale         204833.76  984001.77   0.208 0.835122    
## Type5 ROOM:subzoneRivervale         810247.73 1006350.30   0.805 0.420836    
## years_used:ModelModel A               3443.57     292.15  11.787  < 2e-16 ***
## years_used:ModelModel A2              8458.97    2916.02   2.901 0.003761 ** 
## years_used:ModelPremium Apartment      691.36     345.25   2.002 0.045365 *  
## Type4 ROOM:subzoneCompassvale:Area  -17851.93   10012.15  -1.783 0.074731 .  
## Type5 ROOM:subzoneCompassvale:Area  -23378.48   10162.35  -2.300 0.021521 *  
## Type4 ROOM:subzoneFernvale:Area      -2425.48    4730.96  -0.513 0.608228    
## Type5 ROOM:subzoneFernvale:Area     -11069.70    5322.12  -2.080 0.037656 *  
## Type4 ROOM:subzoneRivervale:Area     -2630.18   14560.30  -0.181 0.856667    
## Type5 ROOM:subzoneRivervale:Area     -7915.74   14661.36  -0.540 0.589322    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27010 on 2037 degrees of freedom
## Multiple R-squared:  0.9054, Adjusted R-squared:  0.9018 
## F-statistic: 253.2 on 77 and 2037 DF,  p-value: < 2.2e-16
BIC(L11)
## [1] 49689.92
L12 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2) +I(Area^3),
         data = df_1)
summary(L12)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type + Model * years_used + I(Area^2) + 
##     I(Area^3), data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -118447  -16203   -1061   15729  118665 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         5.060e+06  1.648e+06   3.069 0.002174 ** 
## Date2022-02-01                      2.396e+03  2.908e+03   0.824 0.410086    
## Date2022-03-01                      9.808e+03  2.813e+03   3.486 0.000500 ***
## Date2022-04-01                      1.783e+04  2.764e+03   6.451 1.39e-10 ***
## Date2022-05-01                      2.341e+04  2.822e+03   8.295  < 2e-16 ***
## Date2022-06-01                      2.878e+04  2.896e+03   9.937  < 2e-16 ***
## Date2022-07-01                      3.328e+04  2.698e+03  12.336  < 2e-16 ***
## Date2022-08-01                      3.657e+04  2.753e+03  13.286  < 2e-16 ***
## Date2022-09-01                      4.625e+04  2.759e+03  16.764  < 2e-16 ***
## Date2022-10-01                      5.402e+04  2.973e+03  18.172  < 2e-16 ***
## Date2022-11-01                      5.692e+04  2.949e+03  19.299  < 2e-16 ***
## Date2022-12-01                      6.316e+04  2.872e+03  21.993  < 2e-16 ***
## Type4 ROOM                          1.520e+06  4.068e+05   3.736 0.000192 ***
## Type5 ROOM                          1.692e+06  6.269e+05   2.699 0.007021 ** 
## years_used                         -9.398e+03  2.842e+02 -33.067  < 2e-16 ***
## subzoneCompassvale                 -1.369e+06  6.939e+05  -1.973 0.048625 *  
## subzoneFernvale                    -8.810e+05  3.433e+05  -2.566 0.010351 *  
## subzoneRivervale                   -4.573e+05  9.887e+05  -0.463 0.643722    
## Story04 TO 06                       2.548e+04  2.151e+03  11.848  < 2e-16 ***
## Story07 TO 09                       4.273e+04  2.128e+03  20.080  < 2e-16 ***
## Story10 TO 12                       5.003e+04  2.199e+03  22.750  < 2e-16 ***
## Story13 TO 15                       5.847e+04  2.132e+03  27.424  < 2e-16 ***
## Story16 TO 18                       6.642e+04  2.655e+03  25.017  < 2e-16 ***
## Story19 TO 21                       6.541e+04  3.994e+03  16.377  < 2e-16 ***
## Story22 TO 24                       7.099e+04  4.466e+03  15.898  < 2e-16 ***
## Story25 TO 27                       6.553e+04  6.179e+03  10.606  < 2e-16 ***
## Area                               -1.480e+05  5.401e+04  -2.741 0.006186 ** 
## ModelModel A                       -3.726e+04  5.172e+03  -7.204 8.19e-13 ***
## ModelModel A2                      -1.886e+05  6.708e+04  -2.811 0.004986 ** 
## ModelPremium Apartment              9.621e+03  5.382e+03   1.788 0.073974 .  
## `ANCHORVALE ST`                     1.423e+04  8.235e+03   1.727 0.084255 .  
## `COMPASSVALE LANE`                 -1.913e+03  1.167e+04  -0.164 0.869791    
## `FERNVALE LINK`                    -2.909e+03  3.348e+03  -0.869 0.385016    
## `FERNVALE ST`                      -6.904e+03  5.570e+03  -1.239 0.215307    
## `RIVERVALE CRES`                    1.463e+04  1.105e+04   1.324 0.185495    
## `ANCHORVALE CRES`                   6.504e+03  7.462e+03   0.872 0.383567    
## `COMPASSVALE CRES`                 -2.302e+04  1.143e+04  -2.014 0.044168 *  
## `SENGKANG EAST AVE`                 7.909e+04  1.209e+04   6.541 7.73e-11 ***
## `SENGKANG WEST AVE`                 9.673e+03  8.373e+03   1.155 0.248147    
## `SENGKANG WEST WAY`                -1.116e+04  4.651e+03  -2.400 0.016473 *  
## `COMPASSVALE DR`                    4.366e+04  1.158e+04   3.772 0.000167 ***
## `JLN KAYU`                         -7.523e+03  8.972e+03  -0.838 0.401874    
## `ANCHORVALE LINK`                   2.642e+04  7.364e+03   3.588 0.000342 ***
## `COMPASSVALE BOW`                   6.850e+04  1.175e+04   5.832 6.36e-09 ***
## `COMPASSVALE ST`                   -1.539e+04  1.132e+04  -1.360 0.173907    
## `COMPASSVALE WALK`                  2.647e+04  1.281e+04   2.066 0.038930 *  
## `RIVERVALE ST`                      5.063e+04  1.325e+04   3.822 0.000136 ***
## `RIVERVALE WALK`                    7.016e+04  1.349e+04   5.202 2.17e-07 ***
## `SENGKANG EAST WAY`                 5.951e+04  8.750e+03   6.801 1.36e-11 ***
## `ANCHORVALE DR`                     5.151e+04  8.640e+03   5.961 2.94e-09 ***
## `RIVERVALE DR`                      5.370e+04  1.133e+04   4.741 2.27e-06 ***
## `ANCHORVALE RD`                     1.204e+04  7.189e+03   1.674 0.094270 .  
## `COMPASSVALE LINK`                  7.390e+04  1.141e+04   6.476 1.18e-10 ***
## `FERNVALE LANE`                    -7.774e+02  6.742e+03  -0.115 0.908216    
## `SENGKANG CTRL`                     8.519e+04  1.211e+04   7.037 2.67e-12 ***
## `COMPASSVALE RD`                    2.222e+04  1.169e+04   1.900 0.057573 .  
## `SENGKANG EAST RD`                  4.333e+03  1.430e+04   0.303 0.761924    
## I(Area^2)                           1.432e+03  5.588e+02   2.563 0.010438 *  
## I(Area^3)                          -3.847e+00  1.797e+00  -2.141 0.032409 *  
## subzoneCompassvale:Area             2.041e+04  1.025e+04   1.992 0.046461 *  
## subzoneFernvale:Area                1.329e+04  5.065e+03   2.624 0.008768 ** 
## subzoneRivervale:Area               6.618e+03  1.469e+04   0.451 0.652362    
## Type4 ROOM:Area                    -1.697e+04  4.724e+03  -3.593 0.000334 ***
## Type5 ROOM:Area                    -1.865e+04  6.703e+03  -2.782 0.005446 ** 
## Type4 ROOM:subzoneCompassvale       1.705e+06  7.085e+05   2.406 0.016202 *  
## Type5 ROOM:subzoneCompassvale       2.312e+06  7.303e+05   3.165 0.001573 ** 
## Type4 ROOM:subzoneFernvale          3.633e+05  3.779e+05   0.961 0.336437    
## Type5 ROOM:subzoneFernvale          1.256e+06  4.862e+05   2.583 0.009861 ** 
## Type4 ROOM:subzoneRivervale         5.902e+05  9.995e+05   0.590 0.554939    
## Type5 ROOM:subzoneRivervale         1.130e+06  1.017e+06   1.112 0.266395    
## years_used:ModelModel A             3.167e+03  3.193e+02   9.918  < 2e-16 ***
## years_used:ModelModel A2            9.856e+03  2.986e+03   3.301 0.000980 ***
## years_used:ModelPremium Apartment   5.766e+02  3.491e+02   1.652 0.098761 .  
## Type4 ROOM:subzoneCompassvale:Area -2.371e+04  1.037e+04  -2.286 0.022335 *  
## Type5 ROOM:subzoneCompassvale:Area -2.851e+04  1.043e+04  -2.733 0.006334 ** 
## Type4 ROOM:subzoneFernvale:Area    -7.623e+03  5.314e+03  -1.435 0.151552    
## Type5 ROOM:subzoneFernvale:Area    -1.674e+04  5.940e+03  -2.818 0.004884 ** 
## Type4 ROOM:subzoneRivervale:Area   -8.306e+03  1.479e+04  -0.562 0.574377    
## Type5 ROOM:subzoneRivervale:Area   -1.298e+04  1.484e+04  -0.875 0.381892    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26980 on 2036 degrees of freedom
## Multiple R-squared:  0.9056, Adjusted R-squared:  0.902 
## F-statistic: 250.5 on 78 and 2036 DF,  p-value: < 2.2e-16
BIC(L12)
## [1] 49692.83
plot(df_1$Area, residuals(L11))

We can use higher term for Area Moving on to years_used

L13 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2) + I(years_used^2),
         data = df_1)
summary(L13)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type + Model * years_used + I(Area^2) + 
##     I(years_used^2), data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -119977  -16328    -987   15539  118966 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                        1494752.80  406696.22   3.675 0.000244 ***
## Date2022-02-01                        2479.51    2901.44   0.855 0.392885    
## Date2022-03-01                        9720.65    2807.38   3.463 0.000546 ***
## Date2022-04-01                       18092.56    2757.91   6.560 6.79e-11 ***
## Date2022-05-01                       23570.34    2817.31   8.366  < 2e-16 ***
## Date2022-06-01                       28647.10    2890.75   9.910  < 2e-16 ***
## Date2022-07-01                       33183.62    2692.59  12.324  < 2e-16 ***
## Date2022-08-01                       36675.89    2747.42  13.349  < 2e-16 ***
## Date2022-09-01                       46012.38    2754.56  16.704  < 2e-16 ***
## Date2022-10-01                       53987.86    2966.44  18.200  < 2e-16 ***
## Date2022-11-01                       56462.59    2947.34  19.157  < 2e-16 ***
## Date2022-12-01                       63315.41    2865.84  22.093  < 2e-16 ***
## Type4 ROOM                          797851.80  262729.62   3.037 0.002422 ** 
## Type5 ROOM                          917360.67  561576.49   1.634 0.102509    
## years_used                          -14059.52    1291.98 -10.882  < 2e-16 ***
## subzoneCompassvale                 -839746.62  669771.05  -1.254 0.210065    
## subzoneFernvale                    -463241.79  300491.76  -1.542 0.123323    
## subzoneRivervale                    240399.84  975958.92   0.246 0.805458    
## Story04 TO 06                        25841.38    2148.32  12.029  < 2e-16 ***
## Story07 TO 09                        43112.81    2126.21  20.277  < 2e-16 ***
## Story10 TO 12                        50312.69    2195.51  22.916  < 2e-16 ***
## Story13 TO 15                        58747.85    2129.50  27.588  < 2e-16 ***
## Story16 TO 18                        66593.05    2650.39  25.126  < 2e-16 ***
## Story19 TO 21                        65286.61    3986.07  16.379  < 2e-16 ***
## Story22 TO 24                        71510.54    4458.23  16.040  < 2e-16 ***
## Story25 TO 27                        66480.28    6172.47  10.770  < 2e-16 ***
## Area                                -30429.26   10766.77  -2.826 0.004756 ** 
## ModelModel A                        -40875.10    5031.11  -8.124 7.71e-16 ***
## ModelModel A2                      -112009.83   65228.83  -1.717 0.086098 .  
## ModelPremium Apartment                9241.35    5352.09   1.727 0.084377 .  
## `ANCHORVALE ST`                      18116.00    8308.85   2.180 0.029347 *  
## `COMPASSVALE LANE`                   11316.44   12232.91   0.925 0.355033    
## `FERNVALE LINK`                      -7743.35    3613.14  -2.143 0.032223 *  
## `FERNVALE ST`                       -11188.02    5684.85  -1.968 0.049199 *  
## `RIVERVALE CRES`                     24452.77   11354.38   2.154 0.031389 *  
## `ANCHORVALE CRES`                     5618.23    7443.48   0.755 0.450465    
## `COMPASSVALE CRES`                  -17498.20   11506.99  -1.521 0.128501    
## `SENGKANG EAST AVE`                  87707.82   12305.42   7.128 1.41e-12 ***
## `SENGKANG WEST AVE`                  12238.13    8397.07   1.457 0.145153    
## `SENGKANG WEST WAY`                 -12855.36    4665.08  -2.756 0.005910 ** 
## `COMPASSVALE DR`                     49251.83   11651.81   4.227 2.47e-05 ***
## `JLN KAYU`                           -6632.87    8959.38  -0.740 0.459187    
## `ANCHORVALE LINK`                    28856.06    7393.52   3.903 9.81e-05 ***
## `COMPASSVALE BOW`                    77549.05   11965.28   6.481 1.14e-10 ***
## `COMPASSVALE ST`                     -9978.65   11380.82  -0.877 0.380701    
## `COMPASSVALE WALK`                   32754.40   12877.78   2.543 0.011049 *  
## `RIVERVALE ST`                       55585.49   13317.47   4.174 3.12e-05 ***
## `RIVERVALE WALK`                     74808.56   13538.83   5.525 3.71e-08 ***
## `SENGKANG EAST WAY`                  62587.04    8791.87   7.119 1.50e-12 ***
## `ANCHORVALE DR`                      53024.01    8636.69   6.139 9.93e-10 ***
## `RIVERVALE DR`                       59854.76   11407.21   5.247 1.71e-07 ***
## `ANCHORVALE RD`                      13282.50    7187.99   1.848 0.064765 .  
## `COMPASSVALE LINK`                   87620.64   11926.73   7.347 2.93e-13 ***
## `FERNVALE LANE`                      -3383.72    6770.82  -0.500 0.617305    
## `SENGKANG CTRL`                      99654.29   12691.56   7.852 6.57e-15 ***
## `COMPASSVALE RD`                     27690.40   11740.94   2.358 0.018446 *  
## `SENGKANG EAST RD`                    8069.47   14316.34   0.564 0.573051    
## I(Area^2)                              219.09      70.80   3.095 0.001998 ** 
## I(years_used^2)                        167.25      46.77   3.576 0.000357 ***
## subzoneCompassvale:Area              12397.76    9883.12   1.254 0.209827    
## subzoneFernvale:Area                  7121.35    4416.40   1.612 0.107012    
## subzoneRivervale:Area                -3906.09   14501.88  -0.269 0.787687    
## Type4 ROOM:Area                      -8661.86    3045.12  -2.845 0.004492 ** 
## Type5 ROOM:Area                      -9663.71    5790.75  -1.669 0.095307 .  
## Type4 ROOM:subzoneCompassvale      1194465.96  683400.23   1.748 0.080645 .  
## Type5 ROOM:subzoneCompassvale      1909271.31  714316.92   2.673 0.007581 ** 
## Type4 ROOM:subzoneFernvale          -53653.26  341481.05  -0.157 0.875166    
## Type5 ROOM:subzoneFernvale          819039.64  448762.10   1.825 0.068131 .  
## Type4 ROOM:subzoneRivervale        -106008.49  985009.16  -0.108 0.914306    
## Type5 ROOM:subzoneRivervale         514383.23 1006855.50   0.511 0.609490    
## years_used:ModelModel A               3527.19     292.24  12.069  < 2e-16 ***
## years_used:ModelModel A2              6611.76    2953.14   2.239 0.025271 *  
## years_used:ModelPremium Apartment      787.80     345.31   2.281 0.022628 *  
## Type4 ROOM:subzoneCompassvale:Area  -15970.82    9997.15  -1.598 0.110301    
## Type5 ROOM:subzoneCompassvale:Area  -21685.21   10144.13  -2.138 0.032659 *  
## Type4 ROOM:subzoneFernvale:Area      -1396.48    4726.09  -0.295 0.767655    
## Type5 ROOM:subzoneFernvale:Area     -10344.39    5310.66  -1.948 0.051570 .  
## Type4 ROOM:subzoneRivervale:Area      2117.43   14578.92   0.145 0.884536    
## Type5 ROOM:subzoneRivervale:Area     -3256.45   14677.06  -0.222 0.824435    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26930 on 2036 degrees of freedom
## Multiple R-squared:  0.906,  Adjusted R-squared:  0.9024 
## F-statistic: 251.6 on 78 and 2036 DF,  p-value: < 2.2e-16
BIC(L13)
## [1] 49684.34
L14 <- lm(ResalePrice ~.- Block-`ANCHORVALE LANE`-`FERNVALE RD`+ Area*subzone*Type +Model*years_used + I(Area^2) + I(years_used^2) + I(years_used^3),
         data = df_1)
summary(L14)
## 
## Call:
## lm(formula = ResalePrice ~ . - Block - `ANCHORVALE LANE` - `FERNVALE RD` + 
##     Area * subzone * Type + Model * years_used + I(Area^2) + 
##     I(years_used^2) + I(years_used^3), data = df_1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -118280  -16373    -839   15409  118408 
## 
## Coefficients:
##                                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         1.528e+06  4.067e+05   3.758 0.000176 ***
## Date2022-02-01                      2.646e+03  2.900e+03   0.913 0.361584    
## Date2022-03-01                      9.845e+03  2.806e+03   3.509 0.000460 ***
## Date2022-04-01                      1.832e+04  2.758e+03   6.643 3.93e-11 ***
## Date2022-05-01                      2.377e+04  2.816e+03   8.439  < 2e-16 ***
## Date2022-06-01                      2.900e+04  2.893e+03  10.024  < 2e-16 ***
## Date2022-07-01                      3.372e+04  2.702e+03  12.479  < 2e-16 ***
## Date2022-08-01                      3.727e+04  2.759e+03  13.506  < 2e-16 ***
## Date2022-09-01                      4.676e+04  2.775e+03  16.851  < 2e-16 ***
## Date2022-10-01                      5.489e+04  2.995e+03  18.330  < 2e-16 ***
## Date2022-11-01                      5.750e+04  2.986e+03  19.259  < 2e-16 ***
## Date2022-12-01                      6.432e+04  2.902e+03  22.161  < 2e-16 ***
## Type4 ROOM                          7.254e+05  2.647e+05   2.740 0.006196 ** 
## Type5 ROOM                          8.318e+05  5.626e+05   1.479 0.139386    
## years_used                         -2.065e+04  3.376e+03  -6.117 1.14e-09 ***
## subzoneCompassvale                 -8.777e+05  6.694e+05  -1.311 0.189989    
## subzoneFernvale                    -4.399e+05  3.004e+05  -1.464 0.143308    
## subzoneRivervale                    3.508e+05  9.765e+05   0.359 0.719435    
## Story04 TO 06                       2.591e+04  2.147e+03  12.070  < 2e-16 ***
## Story07 TO 09                       4.317e+04  2.125e+03  20.319  < 2e-16 ***
## Story10 TO 12                       5.031e+04  2.194e+03  22.936  < 2e-16 ***
## Story13 TO 15                       5.862e+04  2.129e+03  27.537  < 2e-16 ***
## Story16 TO 18                       6.667e+04  2.648e+03  25.174  < 2e-16 ***
## Story19 TO 21                       6.524e+04  3.983e+03  16.382  < 2e-16 ***
## Story22 TO 24                       7.156e+04  4.454e+03  16.064  < 2e-16 ***
## Story25 TO 27                       6.686e+04  6.170e+03  10.836  < 2e-16 ***
## Area                               -3.038e+04  1.076e+04  -2.824 0.004794 ** 
## ModelModel A                       -4.106e+04  5.028e+03  -8.167 5.49e-16 ***
## ModelModel A2                      -1.388e+05  6.639e+04  -2.091 0.036689 *  
## ModelPremium Apartment              1.154e+04  5.457e+03   2.115 0.034576 *  
## `ANCHORVALE ST`                     1.772e+04  8.304e+03   2.133 0.033014 *  
## `COMPASSVALE LANE`                  6.024e+03  1.248e+04   0.483 0.629242    
## `FERNVALE LINK`                    -8.086e+03  3.614e+03  -2.237 0.025362 *  
## `FERNVALE ST`                      -1.091e+04  5.682e+03  -1.920 0.055024 .  
## `RIVERVALE CRES`                    1.638e+04  1.197e+04   1.369 0.171291    
## `ANCHORVALE CRES`                   2.854e+03  7.551e+03   0.378 0.705516    
## `COMPASSVALE CRES`                 -2.433e+04  1.194e+04  -2.037 0.041747 *  
## `SENGKANG EAST AVE`                 8.349e+04  1.246e+04   6.703 2.63e-11 ***
## `SENGKANG WEST AVE`                 1.233e+04  8.390e+03   1.469 0.141963    
## `SENGKANG WEST WAY`                -1.226e+04  4.669e+03  -2.626 0.008692 ** 
## `COMPASSVALE DR`                    4.308e+04  1.200e+04   3.589 0.000340 ***
## `JLN KAYU`                         -5.830e+03  8.960e+03  -0.651 0.515296    
## `ANCHORVALE LINK`                   2.773e+04  7.406e+03   3.745 0.000186 ***
## `COMPASSVALE BOW`                   7.109e+04  1.234e+04   5.761 9.65e-09 ***
## `COMPASSVALE ST`                   -1.426e+04  1.155e+04  -1.234 0.217180    
## `COMPASSVALE WALK`                  2.915e+04  1.298e+04   2.246 0.024826 *  
## `RIVERVALE ST`                      4.974e+04  1.359e+04   3.660 0.000259 ***
## `RIVERVALE WALK`                    7.016e+04  1.370e+04   5.119 3.35e-07 ***
## `SENGKANG EAST WAY`                 5.859e+04  8.986e+03   6.520 8.81e-11 ***
## `ANCHORVALE DR`                     5.059e+04  8.706e+03   5.811 7.17e-09 ***
## `RIVERVALE DR`                      5.381e+04  1.175e+04   4.579 4.95e-06 ***
## `ANCHORVALE RD`                     1.234e+04  7.196e+03   1.714 0.086593 .  
## `COMPASSVALE LINK`                  8.194e+04  1.222e+04   6.708 2.55e-11 ***
## `FERNVALE LANE`                    -5.076e+03  6.812e+03  -0.745 0.456287    
## `SENGKANG CTRL`                     9.435e+04  1.293e+04   7.299 4.14e-13 ***
## `COMPASSVALE RD`                    2.309e+04  1.193e+04   1.936 0.053056 .  
## `SENGKANG EAST RD`                  3.389e+03  1.447e+04   0.234 0.814897    
## I(Area^2)                           2.163e+02  7.075e+01   3.057 0.002265 ** 
## I(years_used^2)                     7.535e+02  2.813e+02   2.679 0.007448 ** 
## I(years_used^3)                    -1.514e+01  7.162e+00  -2.114 0.034674 *  
## subzoneCompassvale:Area             1.299e+04  9.879e+03   1.315 0.188648    
## subzoneFernvale:Area                6.734e+03  4.416e+03   1.525 0.127504    
## subzoneRivervale:Area              -5.466e+03  1.451e+04  -0.377 0.706398    
## Type4 ROOM:Area                    -7.790e+03  3.070e+03  -2.537 0.011249 *  
## Type5 ROOM:Area                    -8.738e+03  5.802e+03  -1.506 0.132235    
## Type4 ROOM:subzoneCompassvale       1.230e+06  6.830e+05   1.801 0.071847 .  
## Type5 ROOM:subzoneCompassvale       1.936e+06  7.138e+05   2.713 0.006732 ** 
## Type4 ROOM:subzoneFernvale         -7.347e+03  3.419e+05  -0.021 0.982857    
## Type5 ROOM:subzoneFernvale          8.475e+05  4.486e+05   1.889 0.059001 .  
## Type4 ROOM:subzoneRivervale        -2.146e+05  9.855e+05  -0.218 0.827645    
## Type5 ROOM:subzoneRivervale         3.905e+05  1.008e+06   0.387 0.698438    
## years_used:ModelModel A             3.539e+03  2.920e+02  12.119  < 2e-16 ***
## years_used:ModelModel A2            7.995e+03  3.022e+03   2.645 0.008225 ** 
## years_used:ModelPremium Apartment   4.989e+02  3.711e+02   1.344 0.178943    
## Type4 ROOM:subzoneCompassvale:Area -1.650e+04  9.992e+03  -1.651 0.098869 .  
## Type5 ROOM:subzoneCompassvale:Area -2.215e+04  1.014e+04  -2.184 0.029045 *  
## Type4 ROOM:subzoneFernvale:Area    -1.773e+03  4.725e+03  -0.375 0.707586    
## Type5 ROOM:subzoneFernvale:Area    -1.043e+04  5.306e+03  -1.965 0.049537 *  
## Type4 ROOM:subzoneRivervale:Area    3.723e+03  1.459e+04   0.255 0.798559    
## Type5 ROOM:subzoneRivervale:Area   -1.522e+03  1.469e+04  -0.104 0.917492    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26910 on 2035 degrees of freedom
## Multiple R-squared:  0.9062, Adjusted R-squared:  0.9026 
## F-statistic: 248.9 on 79 and 2035 DF,  p-value: < 2.2e-16
BIC(L14)
## [1] 49687.36

Based on the BIC, years_used provides a smaller BIC at higher term ^2.

library(fitdistrplus)
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
## Loading required package: survival
fnorm <- fitdist(residuals(L14), "norm")
## Warning in sqrt(diag(varcovar)): NaNs produced
## Warning in sqrt(1/diag(V)): NaNs produced
## Warning in cov2cor(varcovar): diag(.) had 0 or NA entries; non-finite result is doubtful
result <- gofstat(fnorm, discrete = FALSE)
result
## Goodness-of-fit statistics
##                              1-mle-norm
## Kolmogorov-Smirnov statistic 0.03108534
## Cramer-von Mises statistic   0.72967187
## Anderson-Darling statistic   4.62404065
## 
## Goodness-of-fit criteria
##                                1-mle-norm
## Akaike's Information Criterion   49071.16
## Bayesian Information Criterion   49082.47
KScritvalue <-1.36/sqrt(length(df$Date))
KScritvalue
## [1] 0.02956522
summary(fnorm)
## Fitting of the distribution ' norm ' by maximum likelihood 
## Parameters : 
##          estimate Std. Error
## mean 1.358867e-12        NaN
## sd   2.639320e+04        NaN
## Loglikelihood:  -24533.58   AIC:  49071.16   BIC:  49082.47 
## Correlation matrix:
##      mean  sd
## mean    1 NaN
## sd    NaN   1
plot(fnorm)

Since KS statistics = 0.032744 > 0.02956522=Kcrit, we can reject the null hypothesis and thus the data do provide sufficient evidence to show the normal model is the appropriate model.

To test correlation between street and subzone